How Do You Prove:- ( cos x + sin x) ( cos x - sin x ) = 2 cos^ x-1 ??

1 Answer
Apr 18, 2018

See method below

Explanation:

(cosx + sinx)(cosx - sinx) = cos^2x- sin^2x

since cos^2x + sin^2x = 1 => cos^2x + sin^2x - 1 = 0

Adding zero to the expression wont change the value and since cos^2x + sin^2x - 1=0 we can simply add that without changing the value of the expression.

(cosx + sinx)(cosx - sinx) = cos^2x- sin^2x + cos^2x + sin^2x - 1

sin^2x cancels out

(cosx + sinx)(cosx - sinx) = cos^2x + cos^2x - 1
(cosx + sinx)(cosx - sinx) = 2cos^2x - 1