求证sina-sinb=2cos(a+b)/2*sin(a-b)/2这个怎么证明?

问题描述:

求证sina-sinb=2cos(a+b)/2*sin(a-b)/2这个怎么证明?

sina=sin[(a+b)/2+(a-b)/2]=sin(a+b)/2cos(a-b)/2+cos(a+b)/2sin(a-b)/2sinb=sin[(a+b)/2-(a-b)/2]=sin(a+b)/2cos(a-b)/2-cos(a+b)/2sin(a-b)/2两式相减,得:sina-sinb=2cos(a+b)/2sin(a-b)/2...