cos75°*cos15°-sin225°*sin15°的值为?
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/20 07:07:15
cos75°*cos15°-sin225°*sin15°的值为?
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
= 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
cos75°cos15°+sin75°sin15°的值为( )
(cos15°-cos75°)(sin75°+sin15°)=?
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