http://www.jendo.org/wiki1231/index.php?action=history&feed=atom&title=%E5%88%86%E9%A1%9E%3A%E7%87%92%E8%85%A6%E9%A1%8C 2026-04-10T09:27:28Z 本 Wiki 上此頁面的修訂歷史 MediaWiki 1.35.14 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60338&oldid=prev 2025-02-02T00:48:44Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月2日 (日) 00:48 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42" >第42行：</td> <td colspan="2" class="diff-lineno">第42行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&#039;float:right&#039;&gt;&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/a/a2/Diagram_showing_steps_towards_deriving_half-angle_formula_for_cosine.svg&#039; width=400 height=* /&gt;&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&#039;float:right&#039;&gt;&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/a/a2/Diagram_showing_steps_towards_deriving_half-angle_formula_for_cosine.svg&#039; width=400 height=* /&gt;&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;半角公式相關&#039;&#039;&#039;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;半角公式相關&#039;&#039;&#039;&lt;br/&gt;</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:&#039;&#039;&#039;cosθ = 2cos&lt;sup&gt;2&lt;/sup&gt;(θ/2) - 1&#039;&#039;&#039; 之圖形證明</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:如右圖：</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:如右圖：</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 作土黃色三角形(斜邊為&lt;span style=&#039;text-decoration:overline&#039;&gt;BD&lt;/span&gt;)與粉紅色三角形(斜邊為&lt;span style=&#039;text-decoration:overline&#039;&gt;AB&lt;/span&gt;)翻轉對稱。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 作土黃色三角形(斜邊為&lt;span style=&#039;text-decoration:overline&#039;&gt;BD&lt;/span&gt;)與粉紅色三角形(斜邊為&lt;span style=&#039;text-decoration:overline&#039;&gt;AB&lt;/span&gt;)翻轉對稱。</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l51" >第51行：</td> <td colspan="2" class="diff-lineno">第52行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># ∵&lt;span style=&#039;text-decoration:overline&#039;&gt;AF&lt;/span&gt; = &lt;span style=&#039;text-decoration:overline&#039;&gt;AE&lt;/span&gt; - &lt;span style=&#039;text-decoration:overline&#039;&gt;FE&lt;/span&gt; ∴ cosθ = 2cos&lt;sup&gt;2&lt;/sup&gt;(θ/2) - 1</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># ∵&lt;span style=&#039;text-decoration:overline&#039;&gt;AF&lt;/span&gt; = &lt;span style=&#039;text-decoration:overline&#039;&gt;AE&lt;/span&gt; - &lt;span style=&#039;text-decoration:overline&#039;&gt;FE&lt;/span&gt; ∴ cosθ = 2cos&lt;sup&gt;2&lt;/sup&gt;(θ/2) - 1</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/75度三角形求面積.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;&lt;br/&gt;1:2+√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;=2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;:1&lt;/details&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/75度三角形求面積.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;&lt;br/&gt;1:<ins class="diffchange diffchange-inline">(</ins>2+√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;<ins class="diffchange diffchange-inline">)</ins>=<ins class="diffchange diffchange-inline">(</ins>2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;<ins class="diffchange diffchange-inline">)</ins>:1&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/30_45_75度角.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/30_45_75度角.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>左側隱藏直角三角形之高為 1 ，兩個等長的底為 x ，左側隱藏直角三角形之底為(1-(√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;-1))=2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;&lt;br/&gt;左側隱藏三角形為15°75°90°之直角三角形。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>左側隱藏直角三角形之高為 1 ，兩個等長的底為 x ，左側隱藏直角三角形之底為(1-(√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;-1))=2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;&lt;br/&gt;左側隱藏三角形為15°75°90°之直角三角形。</div></td></tr> <!-- diff cache key wiki1231:diff::1.12:old-60337:rev-60338 --> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60337&oldid=prev 2025-02-02T00:19:11Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月2日 (日) 00:19 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l55" >第55行：</td> <td colspan="2" class="diff-lineno">第55行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>左側隱藏直角三角形之高為 1 ，兩個等長的底為 x ，左側隱藏直角三角形之底為(1-(√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;-1))=2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;&lt;br/&gt;左側隱藏三角形為15°75°90°之直角三角形。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>左側隱藏直角三角形之高為 1 ，兩個等長的底為 x ，左側隱藏直角三角形之底為(1-(√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;-1))=2-√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;&lt;br/&gt;左側隱藏三角形為15°75°90°之直角三角形。</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/兩邊兩底角.<del class="diffchange diffchange-inline">jpg</del>&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/兩邊兩底角.<ins class="diffchange diffchange-inline">png</ins>&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>右側邊(18)垂直翻轉 180° 即成為典型的半角公式圖形。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>右側邊(18)垂直翻轉 180° 即成為典型的半角公式圖形。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length.svg&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length.svg&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <!-- diff cache key wiki1231:diff::1.12:old-60336:rev-60337 --> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60336&oldid=prev 2025-02-01T15:27:36Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 15:27 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l76" >第76行：</td> <td colspan="2" class="diff-lineno">第76行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>⑤tan22.5°= 1/(1+√&lt;span style=&#039;text-decoration:overline&#039;&gt;2&lt;/span&gt;) ≈ 0.41421 =&gt; tan45°= 1&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>⑤tan22.5°= 1/(1+√&lt;span style=&#039;text-decoration:overline&#039;&gt;2&lt;/span&gt;) ≈ 0.41421 =&gt; tan45°= 1&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;⑥&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.<del class="diffchange diffchange-inline">jpg</del>&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;⑥&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.<ins class="diffchange diffchange-inline">png</ins>&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 ∠A=18.4° ， 2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 ∠A=18.4° ， 2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td></tr> <!-- diff cache key wiki1231:diff::1.12:old-60335:rev-60336 --> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60335&oldid=prev 2025-02-01T14:57:10Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 14:57 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l88" >第88行：</td> <td colspan="2" class="diff-lineno">第88行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;th&gt;角度&lt;/th&gt;&lt;th&gt;tanA&lt;/th&gt;&lt;th&gt;tan2A&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;th&gt;角度&lt;/th&gt;&lt;th&gt;tanA&lt;/th&gt;&lt;th&gt;tan2A&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;①45°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;①45°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;②36°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;②36°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.726543</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">3.077684</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;③30°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;③30°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.57735</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">1.732</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;④26.5°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;④26.5°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.5</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">4/3</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑤22.5°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑤22.5°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.41421</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">1</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑥18.4°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑥18.4°&lt;/td&gt;&lt;th&gt;1<ins class="diffchange diffchange-inline">/3</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">3/4</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑦18°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑦18°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.32492</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.726543</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑧15°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑧15°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.267949</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0.57735</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑨0°&lt;/td&gt;&lt;th&gt;<del class="diffchange diffchange-inline">1</del>&lt;/th&gt;&lt;th&gt;<del class="diffchange diffchange-inline">∞</del>&lt;/th&gt;&lt;/tr&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;tr&gt;&lt;td&gt;⑨0°&lt;/td&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0</ins>&lt;/th&gt;&lt;th&gt;<ins class="diffchange diffchange-inline">0</ins>&lt;/th&gt;&lt;/tr&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/table&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/table&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;因式分解：&#039;&#039;&#039;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;因式分解：&#039;&#039;&#039;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a&lt;sup&gt;5&lt;/sup&gt;+a&lt;sup&gt;4&lt;/sup&gt;+1</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a&lt;sup&gt;5&lt;/sup&gt;+a&lt;sup&gt;4&lt;/sup&gt;+1</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60334&oldid=prev 2025-02-01T14:29:47Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 14:29 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l85" >第85行：</td> <td colspan="2" class="diff-lineno">第85行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;table class=nicetable&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;th&gt;角度&lt;/th&gt;&lt;th&gt;tanA&lt;/th&gt;&lt;th&gt;tan2A&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;①45°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;②36°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;③30°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;④26.5°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;⑤22.5°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;⑥18.4°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;⑦18°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;⑧15°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;tr&gt;&lt;td&gt;⑨0°&lt;/td&gt;&lt;th&gt;1&lt;/th&gt;&lt;th&gt;∞&lt;/th&gt;&lt;/tr&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;/table&gt;</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;因式分解：&#039;&#039;&#039;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;因式分解：&#039;&#039;&#039;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a&lt;sup&gt;5&lt;/sup&gt;+a&lt;sup&gt;4&lt;/sup&gt;+1</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a&lt;sup&gt;5&lt;/sup&gt;+a&lt;sup&gt;4&lt;/sup&gt;+1</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60333&oldid=prev 2025-02-01T14:16:55Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 14:16 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l72" >第72行：</td> <td colspan="2" class="diff-lineno">第72行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;④tanA=1/2 ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;④tanA=1/2 ，求 tan2A ？&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=4/3 ，此為 3,4,5 三角形 。 2A 對 4 ，約 53.13° 。&lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=4/3 ，此為 3,4,5 三角形 。 <ins class="diffchange diffchange-inline">∠A=26.5° ， </ins>2A 對 4 ，約 53.13° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9e/Half-angle_formula_side_length_3_4_5.svg&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9e/Half-angle_formula_side_length_3_4_5.svg&#039; width=400 height=* /&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>⑤tan22.5°= 1/(1+√&lt;span style=&#039;text-decoration:overline&#039;&gt;2&lt;/span&gt;≈ 0.41421 =&gt; tan45° = 1&lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>⑤tan22.5°= 1/(1+√&lt;span style=&#039;text-decoration:overline&#039;&gt;2&lt;/span&gt;<ins class="diffchange diffchange-inline">) </ins>≈ 0.41421 =&gt; tan45°= 1&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;⑥&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;⑥&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 <ins class="diffchange diffchange-inline">∠A=18.4° ， </ins>2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60332&oldid=prev 2025-02-01T14:07:44Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 14:07 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l60" >第60行：</td> <td colspan="2" class="diff-lineno">第60行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a 以 18 代入， b 以 30 代入，得出高為 5√&lt;span style=&#039;text-decoration:overline&#039;&gt;11&lt;/span&gt; ， 18 為斜邊的直角三角形底為 7 ，大三角形底 32 ，面積 80√&lt;span style=&#039;text-decoration:overline&#039;&gt;11&lt;/span&gt; 。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a 以 18 代入， b 以 30 代入，得出高為 5√&lt;span style=&#039;text-decoration:overline&#039;&gt;11&lt;/span&gt; ， 18 為斜邊的直角三角形底為 7 ，大三角形底 32 ，面積 80√&lt;span style=&#039;text-decoration:overline&#039;&gt;11&lt;/span&gt; 。</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<del class="diffchange diffchange-inline">tanA</del>=1 ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<ins class="diffchange diffchange-inline">①tanA</ins>=1 ，求 tan2A ？&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=∞ ， ∠A=45° ，2A=90° 。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=∞ ， ∠A=45° ，2A=90° 。</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l67" >第67行：</td> <td colspan="2" class="diff-lineno">第67行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°-sin-cos.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°-sin-cos.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">tan36°≈ </del>0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">②tan36°≈ </ins>0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<del class="diffchange diffchange-inline">tanA</del>=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<ins class="diffchange diffchange-inline">③tanA</ins>=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈1.732)， ∠A=30° ，2A=60° 。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈1.732)， ∠A=30° ，2A=60° 。</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<del class="diffchange diffchange-inline">tanA</del>=1/2 ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<ins class="diffchange diffchange-inline">④tanA</ins>=1/2 ，求 tan2A ？&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=4/3 ，此為 3,4,5 三角形 。 2A 對 4 ，約 53.13° 。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=4/3 ，此為 3,4,5 三角形 。 2A 對 4 ，約 53.13° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9e/Half-angle_formula_side_length_3_4_5.svg&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9e/Half-angle_formula_side_length_3_4_5.svg&#039; width=400 height=* /&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">⑤tan22.5°= 1/(1+√&lt;span style=&#039;text-decoration:overline&#039;&gt;2&lt;/span&gt;≈ 0.41421 =&gt; tan45° = 1&lt;br/&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<ins class="diffchange diffchange-inline">⑥</ins>&lt;img src=&#039;http://jendo.org/files/解數學題/tan_2a.jpg&#039; width=400 height=* /&gt;&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=3/4 ，此為 3,4,5 三角形 。 2A 對 3 ，約 36.87° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/9/9b/Half-angle_formula_side_length_4_3_5.svg&#039; width=400 height=* /&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">tan18°≈ </del>0.32492 =&gt; tan36°≈ 0.726543 &lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">⑦tan18°≈ </ins>0.32492 =&gt; tan36°≈ 0.726543 &lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<del class="diffchange diffchange-inline">tanA</del>=1/(2+√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;)≈0.267949 ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;<ins class="diffchange diffchange-inline">⑧tanA</ins>=1/(2+√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;)≈0.267949 ，求 tan2A ？&lt;/summary&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735)， ∠A=15° ，2A=30° 。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735)， ∠A=15° ，2A=30° 。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;https://upload.wikimedia.org/wikipedia/commons/1/14/15°75°90°triangle_sides.png&#039; width=400 height=* /&gt;</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60331&oldid=prev 2025-02-01T13:53:42Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 13:53 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66" >第66行：</td> <td colspan="2" class="diff-lineno">第66行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°-sin-cos.png&#039; width=400 height=* /&gt;&lt;br/&gt;</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan36°≈ 0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan36°≈ 0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;tanA=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;tanA=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60330&oldid=prev 2025-02-01T13:04:32Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 13:04 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l63" >第63行：</td> <td colspan="2" class="diff-lineno">第63行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=∞ ， ∠A=45° ，2A=90° 。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan2A=2tanA/(1-tan&lt;sup&gt;2&lt;/sup&gt;A)=∞ ， ∠A=45° ，2A=90° 。</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/details&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/values-of-sin-18-cos-18-sin-36-cos-36-sin-54-cos-54.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/values-of-sin-18-cos-18-sin-36-cos-36-sin-54-cos-54.png&#039; width=400 height=* /&gt;<ins class="diffchange diffchange-inline">[https://physicscatalyst.com/article/values-of-sin-18-cos-18-cos-72-sin-36-cos-36-sin-54/ 公式解說(英文)]</ins>&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> </table>

丁志仁 http://www.jendo.org/wiki1231/index.php?title=%E5%88%86%E9%A1%9E:%E7%87%92%E8%85%A6%E9%A1%8C&diff=60329&oldid=prev 2025-02-01T13:00:43Z

<p><span dir="auto"><span class="autocomment">中學數學題</span></span></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="zh-Hant-TW"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年2月1日 (六) 13:00 的修訂</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l65" >第65行：</td> <td colspan="2" class="diff-lineno">第65行：</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/values-of-sin-18-cos-18-sin-36-cos-36-sin-54-cos-54.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/values-of-sin-18-cos-18-sin-36-cos-36-sin-54-cos-54.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;img src=&#039;http://jendo.org/files/解數學題/value-15°-to-75°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;img src=&#039;http://jendo.org/files/解數學題/value-18°-to-72°.png&#039; width=400 height=* /&gt;&lt;br/&gt;</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan36°≈ 0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>tan36°≈ 0.726543 =&gt; tan72°≈ 3.077684 &lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;tanA=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;details&gt;&lt;summary&gt;tanA=1/√&lt;span style=&#039;text-decoration:overline&#039;&gt;3&lt;/span&gt;(≈0.57735) ，求 tan2A ？&lt;/summary&gt;</div></td></tr> </table>

丁志仁