## haleyking345 2 years ago Verifying Trigonometric Identities 1.) cos^2 x-sin^2 x answer:1-2sin^2 x 2.) cos^2 x-sin^2 x answer= 2cos^2 x -1 This is confusing. Both problems start the same but equal different things. How would you solve these?

They both start from: $\cos^2(x) - \sin^2(x)$ We also know:$\cos^2(x) + \sin^2(x) = 1$ Now we can either substitute $1 - \cos^2(x) =\sin^2(x)$or $1 - \sin^2(x) = \cos^2(x)$ Depending on which substitution we do, we get either (Substitution 1):$\cos^2(x) - (1 - \cos^2(x)) = 2\cos^2(x) - 1$ or (Substitution 2):$(1 - \sin^2(x)) - \sin^2(x) = 1 - 2\sin^2(x)$