Question

Question #5c3be

Answer 1

`RHS=sin(x+y)sin(x-y)`

`=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)`

`=sin^2xcos^2y-cos^2xsin^2y`

`=sin^2x(1-sin^2y)-(1-sin^2x)sin^2y`

`=sin^2x-sin^2xsin^2y-sin^2y+sin^2xsin^2y`

`=sin^2x-sin^2y=LHS`

Proved