Prove sin(α+β)sin(α-β)=cos^2β-cos^2α

Answer 1

First off these are usually not this hard...just saying...ill be changing your alphas to x's and your betas to y's

we will work with the left side because it is easier.

use identity sum and difference
sin(x+y)sin(x+y)=cos^2y-cos^2x
s

Answer 2

(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)=
Then, foil those and your middle two terms should cancel out leaving you with
sin^2xcos^2y-cos^2xsin^2y=
now using the pythagereom theorem change all the sin^2's to cos^2 giving you
cos^2y-cos^2xcos^2y-[cos^2xcos^2xcos^2y]=

cos^2y-cos^2xcos^2y-cos^2x+cos^2xcos^2y=

cos^2y-cos^2x