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Math Help - Proving an identity that's proving to be complex

  1. #1
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    Proving an identity that's proving to be complex

    Prove the identity cot A/2 - tan A/2 = 2cot A

    I have written it as:

     \frac{cos \frac{A}{2}}{sin \frac{A}{2}} - \frac { sin \frac {A}{2}}{cos \frac{A}{2}}

    Taking LCM:

     \frac {cos^2 \frac{A}{2} - sin^2 \frac{A}{2}}{sin \frac{A}{2} cos \frac{A}{2}}

    Now I don't know how to solve it any further?

    Is there any easier method of proving this identity ?
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  2. #2
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    Quote Originally Posted by struck View Post
    Prove the identity cot A/2 - tan A/2 = 2cot A

    I have written it as:

     \frac{cos \frac{A}{2}}{sin \frac{A}{2}} - \frac { sin \frac {A}{2}}{cos \frac{A}{2}}

    Taking LCM:

     \frac {cos^2 \frac{A}{2} - sin^2 \frac{A}{2}}{sin \frac{A}{2} cos \frac{A}{2}}

    Now I don't know how to solve it any further?

    Is there any easier method of proving this identity ?
    I'd do it your way too and you were only two steps away from the end. Carrying on:

    For the numerator recall that cos(2u) = cos^2(u) - sin^2(u)

    For the denominator recall that sin(2u) = 2sin(u)cos(u) \rightarrow cos(u)sin(u) = \frac{1}{2}sin(2u)

    This will reduce your equation to \frac{cos(2u)}{\frac{1}{2}sin(2u)} which I'm sure you can simplify to get the answer
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