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haleyking345
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):\[(1 - \sin^2(x)) - \sin^2(x) = 1 - 2\sin^2(x)\]