sinx+siny=2/5,cosx+cosy=6/5,求cos(2x-2y)
问题描述：
sinx+siny=2/5,cosx+cosy=6/5,求cos(2x-2y)
答
cos(2x-2y)=cos2(x-y)=2cos^2(x-y)-1
cos(x-y)=cosxcosy+sinxsiny
(sinx+siny)^2=sin^2x+sin^2y+2sinxsiny=4/25 ………………1
(cosx+cosy)^2=cos^2x+cos^2y+2cosxcosy=36/25………………2
1+2 得
2+2cos(x-y)=8/5
cos(x-y)=-1/5
则cos(2x-2y)=-23/25
写得好辛苦~~