求cos(20°+x)cos(25°-x)-cos(70°-x)sin(155°+x)

问题描述:

求cos(20°+x)cos(25°-x)-cos(70°-x)sin(155°+x)

cos(20°+x) = sin(70°-x)
cos(25°-x) = -cos(155°+x)
原式
= -(sin(70°-x)cos(155°+x)+cos(70°-x)sin(155°+x))
= -(sin(70°-x+155°+x))
= -sin225°
= sin45°
= 根号2 / 2