Trig
posted by Alice on .
Sin(Xy)sin(x+y)=sin^2 x  sin^2 y
work on one side only...so i worked on the right
=(sinxsiny)(sinx+siny) does that equal
sin(xy)sin(x+y)??? help!

Use the formulas for sin (AB) and sin (A+B)
The left side is
(sinx cos y  siny cosx)(sinx cosy + siny cosx)
= sin^2x cos^2y  sin^2y cos^2 x
=(1  cos^2x)(cos^2y)sin^2y cos^2x
= cos^2y cos^2y cos^2x  sin^2y cos^2x
= cos^2y cos^2x
= 1sin^2y 1 + sin^2x
= sin^2x  sin^2y