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Math Help - Proving trig equation

  1. #1
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    Proving trig equation

    I'm having trouble proving trig identities. Especially when the answers don't seem too obvious (you know, cancel something out here, cancel something out there, and then there's the answer). Here's the question I'm stuck on:

    \frac{\sin2\theta}{2-2\cos^2\theta}= \cot\theta

    If anyone can help, that would be appreciated!
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  2. #2
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    \frac{\sin2\theta}{2-2\cos^2\theta}= \cot\theta

    In this equation, try replacing \sin2\theta with its identity = 2\sin\theta\cos\theta
    In the denominator, try factoring out the 2 and seeing what the equation could be equal to.
    Recall \sin^2\theta + \cos^2\theta = 1
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  3. #3
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    Quote Originally Posted by cuteangel View Post
    \frac{\sin2\theta}{2-2\cos^2\theta}= \cot\theta

    In this equation, try replacing \sin2\theta with its identity = 2\sin\theta\cos\theta
    In the denominator, try factoring out the 2 and seeing what the equation could be equal to.
    Recall \sin^2\theta + \cos^2\theta = 1
    So I get 2-2\sin^2\theta on the bottom?
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  4. #4
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    Well, not exactly.
    2 - 2\cos^2\theta = 2(1 - cos^2\theta)
    Now, rearranging \sin^2\theta + \cos^2\theta = 1 gives
    1 - \cos^2\theta = \sin^2\theta
    If you substitute this value in now, the equation should be solvable.
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  5. #5
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    Can you take out a common factor in the denominator? Can it be simplified using the Pythagorean Identity?
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