Prove:

Question

sin(x–y)sin(x+y)=sin^2(x)–sin^2(y)

Answer 1

(sinx cosy - cosx siny)(sinx cosy + cosx siny)
= sin^2x cos^2y - cos^2x sin^2y
= sin^2x(1-sin^2y) - (1-sin^2x)sin^2y
= sin^2x - sin^2x sin^2y - sin^2y + sin^2x sin^2y
= sin^2x - sin^2y