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

1 Answer
Carl S.
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#

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