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Math Help - How to prove as an identity?

  1. #1
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    How to prove as an identity?

    how do i prove that this is an identity?
    \frac{tan^2\theta}{1+tan^2\theta}+\frac{cot^3\thet  a}{1+cot^2\theta}=\frac{1-2sin^2\theta cos^2\theta}{sin\theta cos\theta}
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  2. #2
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    Talking

    The left-hand side, having two fractions, is (or at least looks to be) more complicated than the right-hand side, so try working on the left-hand side.

    A good start would probably be to convert everything to sines and cosines, convert to a common denominator, combine the two fractions, and see where that leads....
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  3. #3
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    ok but does 1+cot\theta equal to 1-2sin^2\theta cos^2\theta ?
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  4. #4
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    Quote Originally Posted by crosser43 View Post
    ok but does 1+cot\theta equal to 1-2sin^2\theta cos^2\theta ?
    <br />
1+cot(x) = 1+\frac{cos(x)}{sin(x)} = \frac{cos(x)+sin(x)}{sin(x)}

    You may recall that 1+tan^2(x) = sec^2(x) and 1+cot^2(x) = csc^2(x)
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