cos75°*cos15°-sin225°*sin15°的值为?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 03:33:28
cos75°*cos15°-sin225°*sin15°的值为?cos75°*cos15°-sin225°*sin15°的值为?cos75°*cos15°-sin225°*sin15°的值为?cos7

cos75°*cos15°-sin225°*sin15°的值为?
cos75°*cos15°-sin225°*sin15°的值为?

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