Posted by **Katie** on Monday, March 5, 2012 at 8:23pm.

Prove sin(α+β)sin(α-β)=cos^2β-cos^2α

- Trig -
**john**, Friday, March 9, 2012 at 6:35pm
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

- Trig -
**john**, Friday, March 9, 2012 at 6:41pm
(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

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