作业帮cos75°cos15°-sin225°sin15°的值为应为cos75°cos15°-sin255°sin15°不好意思
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 12:55:16
cos75°cos15°-sin225°sin15°的值为应为cos75°cos15°-sin255°sin15°不好意思
cos75°cos15°-sin225°sin15°的值为
应为cos75°cos15°-sin255°sin15°
不好意思
cos75°cos15°-sin225°sin15°的值为应为cos75°cos15°-sin255°sin15°不好意思
cos75°cos15°-sin255°sin15°
=cos75°cos15°+sin75°sin15°
=cos(75°-15°).cos的两角差公式
=cos60°
=1/2
cos75°*cos15°-sin225°*sin15°
= cos75°*cos15°- sin(180°+ 45°)*sin15°
= cos75°*cos15°+ sin45°*sin15°
= (√6-√2)/4 × (√6+√2)/4 + √2/2 × (√6-√2)/4
= (6-2)/16 + √2/2 × (√6-√2)/4
= 1...
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cos75°*cos15°-sin225°*sin15°
= cos75°*cos15°- sin(180°+ 45°)*sin15°
= cos75°*cos15°+ sin45°*sin15°
= (√6-√2)/4 × (√6+√2)/4 + √2/2 × (√6-√2)/4
= (6-2)/16 + √2/2 × (√6-√2)/4
= 1/4 + √2/2 × (√6-√2)/4
= 1/4 + (√12-√4)/8
= 1/4 + (2√3-2)/8
= 1/4 + (√3-1)/4
= √3/4
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cos75°cos15°-sin255°sin15°
=sin15°cos15°+sin75°sin15°
=sin15°cos15°+cos15°sin15°
=sin（15°+15°）
=sin30°
=1/2