Question

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

Answer 1

sina=sin[(a＋b)/2＋(a－b)/2]=sin(a＋b)/2cos(a－b)/2＋cos(a＋b)/2sin(a－b)/2
sinb=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

Answer 2

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
=...