cos(x+y)-cosx为什么等于-2sin（x+y/2)2siny/2写错了,后面不是2siny/2是siny/2

Question

cos(x+y)-cosx为什么等于-2sin（x+y/2)2siny/2
写错了,后面不是2sin y/2是siny/2

Answer 1

cos(x+y)-cosx=cos[(2x+y)/2+(y/2)]-cos[(2x+y)/2-(y/2)]
=cos[(2x+y)/2]*cos(y/2)-sin[(2x+y)/2]*sin(y/2)-cos[(2x+y)/2]*cos(y/2)-sin[(2x+y)/2]*sin(y/2)
=-2sin[(2x+y)/2]sin(y/2)