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Math Help - Trig equations

  1. #1
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    Trig equations

    I got stuck in these 2 equations :

    tan^{2}x=\frac{1-cosx}{1-sin\left | x \right |}
    \left | log_{\frac{1}{3}}(1+sin2x) \right |+\left | log_{\frac{1}{3}}(1-sin2x)\right |=1
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  2. #2
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    Quote Originally Posted by ldx2 View Post
    I got stuck in these 2 equations :

    tan^{2}x=\frac{1-cosx}{1-sin\left | x \right |}
    \left | log_{\frac{1}{3}}(1+sin2x) \right |+\left | log_{\frac{1}{3}}(1-sin2x)\right |=1
    second one: you can combine those two expressions into a single log.

    | \log_{1/3}\left[(1+sin[2x])(1-sin[2x])\right) |

    Which is the difference of two squares

    = \log_{1/3} \left(1-sin^2(2x)\right) = \log_{1/3} cos^2(2x)

    This is equal to 1

    \log_{1/3} cos^2(2x) = \pm 1

    cos^2(2x) = \frac{1}{3} or cos^2(2x) = 3

    The second solution is not a solution because cos^2(2x) cannot be 3
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