一道三角恒等式证明题请证明sin(x+y)sin(x-y)=sin^2(x)-sin^2(y)

左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=sin²xcos²y-cos²xsin²y
=sin²x(1-sin²y)-(1-sin²x)sin²y
=sin²x-sin²xsin²y+sin²xsin²y-sin²y
=sin²x-sin²y
=右边