求推导sinx-siny=2cos（(x+y)/2)sin((x-y)/2)
问题描述：
求推导sinx-siny=2cos（(x+y)/2)sin((x-y)/2)
答
cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
(x+y)/2=α (x-y)/2=β
2cos（(x+y)/2)sin((x-y)/2)=2*[1/2(sinx-siny)]=sinx-siny
答
sin((x+y)/2+(x-y)/2)-sin((x+y)/2-(x-y)/2)
化简出来就是了
答
用积化和差公式cosαsinβ= 1/2[sin(α+β)-sin(α-β)]
(x+y)/2=α (x-y)/2=β代入上式
得到2cos（(x+y)/2)sin((x-y)/2)=2*[1/2(sinx-siny)]=sinx-siny