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?
答
令x=(a+b)/2,y=(a-b)/2
则a=x+y,b=x-y
sina-sinb
=sin(x+y)-sin(x-y)
=sinxcosy+cosxsiny-[sinxcosy-cosxsiny]
=2cosxsiny
=...
答
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...