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)
答
cos(20+x)cos(25-x)-cos(70-x)sin(155+x)
=(1/2)[cos45+cos(2x-5)]-(1/2)[sin225+sin(2x+85)]
=(1/2)[cos45+sin45]+(1/2)[cos(2x-5)-sin(2x+85)]
=(根号2/2)+(1/2)[sin[90+(2x-5)]-sin(2x+85)]
=(根号2/2)+(1/2)[sin(85+2x)-sin(2x+85)]
=根号2/2
答
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