如果cosx+cosy-cos(x+y)=0,x,y为锐角,求x和y.

问题描述:

如果cosx+cosy-cos(x+y)=0,x,y为锐角,求x和y.

由cosx+cosy-cos(x+y)=0,得cosx+cosy=cos(x+y)
即cosx+cosy=cosxcosy-sinxsiny,化简得
(1-cosx)(1-cosy)=1+sinxsiny>1,(x,y为锐角)
而1-cosx