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## Homework Statement

cos(α − β)cos(α + β) = cos

^{2}α - sin

^{2}β

## Homework Equations

cos(α + β) = cos α cos β − sin α sin β

cos(α − β) = cos α cos β + sin α sin β

## The Attempt at a Solution

I worked out the LHS which makes it

cos

^{2}α cos

^{2}β - sin

^{2}α sin

^{2}β=RHS

Then, I'm stuck, however, i tried to do what I think can work...But I don't think it's right.

From here I think it's wrong.

(cos

^{2}α - sin

^{2}β) (cos

^{2}β + sin

^{2}α)=RHS

(cos

^{2}α - sin

^{2}β) (1) =RHSS

My problem is can we use identity for items like cos

^{2}a + sin

^{2}B = 1?

the variable is not the same :/