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Math Help - [SOLVED] solve equation

  1. #1
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    [SOLVED] solve equation

    sin2theta-1=cos2theta
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Jaffa View Post
    sin2theta-1=cos2theta
    \sin 2 \theta-1=\cos 2 \theta

    Substitute double angle identities:

    \boxed{\sin 2 \theta = 2 \sin \theta \cos \theta}

    \boxed{\cos 2 \theta = 1 - 2 \sin^2 \theta}

    2 \sin \theta \cos \theta - 1 = 1 - 2 \sin^2 \theta

    2 \sin^2 \theta + 2 \sin \theta \cos \theta-2=0

    {\color{red}\sin^2 \theta}+ \sin \theta \cos \theta {\color{red}- 1} = 0

    Identity: Since \sin^2 \theta+ \cos^2 \theta=1, then
    \boxed{{\color{red}\sin^2 \theta - 1 = -\cos^2 \theta}}

    -\cos^2 \theta+ \sin \theta \cos \theta=0

    \cos^2 \theta-\sin \theta \cos \theta=0

    \cos \theta(1-\sin \theta)=0

    \boxed{\cos \theta = 0} \ \ or \ \ 1-\sin \theta=0

    -\sin \theta = -1

    \boxed{\sin \theta=1}

    \cos \theta=0 \ \ at \ \ \left\{\frac{\pi}{2}, \frac{3\pi}{2}\right\}

    \sin \theta = 1 \ \ at \ \ \left\{\frac{\pi}{2}\right\}

    Solution set = \left\{\frac{\pi}{2}, \frac{3\pi}{2}\right\}
    Last edited by masters; December 16th 2008 at 09:47 AM.
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