证明sin(x+y)sin(x-y)=(sinx)^2-(siny)^2.

问题描述:

证明sin(x+y)sin(x-y)=(sinx)^2-(siny)^2.

sin(x+y)sin(x-y)
=-1/2(cos(x+y+x-y)—cos(x+y-x+y))
=-1/2(cos2x—cos2y)
=-1/2(1-2(sinx)^2-1+2(siny)^2)
=(sinx)^2-(siny)^2