trig
posted by Carl .
Prove:
sin(x–y)sin(x+y)=sin^2(x)–sin^2(y)

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