Question

Sin(X-y)sin(x+y)=sin^2 x - sin^2 y

work on one side only...so i worked on the right

=(sinx-siny)(sinx+siny) does that equal
sin(x-y)sin(x+y)??? help!

Answer 1

Use the formulas for sin (A-B) 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
= 1-sin^2y -1 + sin^2x
= sin^2x - sin^2y