sin(x-y)sin(x+y)=cos^2y-cos2^x
Л.Ч.
sin(x-y)sin(x+y)=sin(x+(-y))sin(x+y)=
=(sinx cosy + siny cosx)*(sinx cos(-y) + sin(-y) cosx)=
=(sinx cosy + siny cosx)*(sinx cosy - siny cosx)=
=sin^2 x cos^2y - siny cosy sinx cosx - sin^2 y cos^2x + siny cosy sinx cosx=
=sin^2 x cos^2y - sin^2 y cos^2x = ( 1- cos^2x)cos^2y -(1- cos^2y) cos^2x=
=cos^2y- cos^2y cos^2x- cos^2x+ cos^2y cos^2x=cos^2y-cos2^x
Л.Ч=П.Ч
sin(x-y)sin(x+y)=cos^2y-cos2^x
Тождество доказанно
