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Math Help - Trigonometric identity

  1. #1
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    [SOLVED] Trigonometric identity

    I'm trying to verify that:
    -tan^2(x) is the same as (sec^2(x)) * (-sin^2(x))

    But I get:
    -tan^2(x) = -(sec^2(x) - 1)

    Where does the sin^2(x) come from?
    Last edited by daigo; June 8th 2012 at 04:24 AM.
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  2. #2
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    Re: Trigonometric identity

    Quote Originally Posted by daigo View Post
    I'm trying to verify that:
    -tan^2(x) is the same as (sec^2(x)) * (-sin^2(x))

    But I get:
    -tan^2(x) = -(sec^2(x) - 1)

    Where does the sin^2(x) come from?
    \displaystyle \begin{align*} \sec^2{x}\left(-\sin^2{x}\right) &\equiv \frac{1}{\cos^2{x}}\left(-\sin^2{x}\right) \\ &\equiv -\frac{\sin^2{x}}{\cos^2{x}} \\ &\equiv -\tan^2{x}  \end{align*}
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