Question

cos75°cos15°-sin225°sin15°的值为

题目错了，应为cos75°cos15°-sin255°sin15°
不好意思

Answer 1

cos75°cos15°-sin255°sin15°
=cos75°cos15°+sin75°sin15°
=cos(75°-15°)...........................cos的两角差公式
=cos60°
=1/2

Answer 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
= 1/4 + √2/2 × (√6-√2)/4
= 1/4 + (√12-√4)/8
= 1/4 + (2√3-2)/8
= 1/4 + (√3-1)/4
= √3/4

Answer 3

cos75°cos15°-sin255°sin15°
=sin15°cos15°+sin75°sin15°
=sin15°cos15°+cos15°sin15°
=sin（15°+15°）
=sin30°
=1/2