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 2 years ago
Verifying Trigonometric Identities
1.) cos^2 xsin^2 x
answer:12sin^2 x
2.) cos^2 xsin^2 x
answer= 2cos^2 x 1
This is confusing. Both problems start the same but equal different things. How would you solve these?
 2 years ago
Verifying Trigonometric Identities 1.) cos^2 xsin^2 x answer:12sin^2 x 2.) cos^2 xsin^2 x answer= 2cos^2 x 1 This is confusing. Both problems start the same but equal different things. How would you solve these?

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daniel987600
 2 years ago
Best ResponseYou've already chosen the best response.1They 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):\[(1  \sin^2(x))  \sin^2(x) = 1  2\sin^2(x)\]
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