证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin(x-y)/2

题目应该是“证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin²(x-y)/2”
Pr：
左边展开得
cos²x-cosxcosy+sin²x-sinxsiny
=1-(cosxcosy+sinxsiny)
=1-cos(x-y)
=1-cos²(x-y)/2+sin²(x-y)/2
=2sin²(x-y)/2
=右边