$sin(x+y).(sin(x-y)\\=(sinx.cosy+siny.cosx).(sinx.cosy-siny.cosx)(1)\\=sin^2x(1-sin^2y)-sin^2y(1-sin^2x)\\=sin^2x-sin^2y.sin^2x-sin^2y+sin^2y.sin^2x=sin^2x-sin^2y\\\text{Từ (1) ta có :}\\(1-cos^2x).cos^2y-(1-cos^2y).cos^2x\\=cos^2y-cos^2x$
$Cos(x+y).Cos(x-y)\\=(cosx.cosy-sinx.siny).(cosx.cosy+sinx.siny)(2)\\=cos^2x(1-sin^2y)-(1-cos^2x)sin^2y\\=cos^2x-sin^2y\\\text{Từ (2) ta có :}\\=(1-sin^2x)cos^2y-(1-cos^2y).sin^2x\\=cos^2y-sin^2x$
