为什么cos2x+cos2y=2cos(x+y)cos(x-y)

问题描述:

为什么cos2x+cos2y=2cos(x+y)cos(x-y)

cos2x=cos(x+y+x-y)=cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
cos2y=cos(x+y-x+y)=cos(x+y)cos(x-y)+sin(x+y)sin(x-y)
相加即有cos2x+cos2y=2cos(x+y)cos(x-y)

2x=(x+y)+(x-y)
2y=(x+y)-(x-y)
cos2x=cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
cos2y=cos(x+y)cos(x-y)+sin(x+y)sin(x-y)
cos2x+cos2y=2cos(x+y)cos(x-y)