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Math Help - Prove the identity

  1. #1
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    Question [Solved] Prove the identity

    Hey, could some one help me prove the following identity?

    <br />
\sec \theta + \csc \theta - \cos \theta - \sin \theta = \sin \theta * \tan \theta + \cos \theta * \cot \theta<br />
    Last edited by gordo151091; August 25th 2010 at 02:01 PM.
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  2. #2
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    Quote Originally Posted by gordo151091 View Post
    Hey, could some one help me prove the following identity?

    <br />
\sec \theta + \csc \theta - \cos \theta - \sin \theta = \sin \theta * \tan \theta + \cos \theta * \cot \theta<br />
    Just combine the terms on the LHS, creating common denominators...

    \displaystyle\frac{1}{Cos\theta}+\frac{1}{Sin\thet  a}-\left(Cos\theta+Sin\theta\right)=\frac{Sin\theta+C  os\theta}{Cos\theta\,Sin\theta}-\frac{Cos^2\theta\,Sin\theta+Sin^2\theta\,Cos\thet  a}{Cos\theta\,Sin\theta}

    =\displaystyle\frac{Sin\theta\left(1-Cos^2\theta\right)+Cos\theta\left(1-Sin^2\theta\right)}{Sin\theta\,Cos\theta}=\frac{Si  n^3\theta+Cos^3\theta}{Sin\theta\,Cos\theta}

    Simplifying that is all that's required.
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  3. #3
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    Thanks! I finally saw the mistake I was repeating over and over...
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