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Math Help - Identities Problem

  1. #1
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    Identities Problem

    How someone help me prove the identity below?

    (1-tan^2X)(1-cos^2X)=[(sin^2X-4sin^4X)/(1-sin^2X)]

    Thanks in advance! =)
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  2. #2
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    Hello Hellooo

    Welcome to Math Help Forum!
    Quote Originally Posted by Hellooo View Post
    How someone help me prove the identity below?

    (1-tan^2X)(1-cos^2X)=[(sin^2X-4sin^4X)/(1-sin^2X)]

    Thanks in advance! =)
    I think the 4 on the RHS should be a 2. Here's my answer:

    (1-\tan^2x)(1-\cos^2x)
    =\left(1-\frac{\sin^2x}{\cos^2x}\right)\sin^2x, using \tan x = \frac{\sin x}{\cos x} and 1 - \cos^2x = \sin^2 x

    =\frac{(\cos^2x-\sin^2x)\sin^2x}{\cos^2x}

    =\frac{(1-2\sin^2x)\sin^2x}{1-\sin^2x}, using \cos^2x =1-\sin^2x

    =\frac{\sin^2x-2\sin^4x}{1-\sin^2x}
    Grandad
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  3. #3
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    Oh thanks,
    I was thinking..why was there a 4 there..
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