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Math Help - Identity problem

  1. #1
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    Apr 2010
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    Identity problem

    Prove that the left equals the right
    1-(sin^2x)/(1+cotx)-(cos^2x)/(1+tanx) = sin2x/2


    So far I've multiplied to get a common denominator of  1+tanx+cotx+cotxtanx And have the numerator of cotx+tanx+cotxtanx Past this I can't think of where to go.
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  2. #2
    Junior Member
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    Oct 2008
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    I will use s & c for sine and cosine respectively.

    First convert the LHS to sines and cosines:

    1 - \frac{s^2}{1+c/s} - \frac{c^2}{1 + s/c}

    Now simplify a bit:

    1 - \frac{s^3}{s+c} - \frac{c^3}{s+c}

    Put everything into one fraction and use the sum of cubes factorization:

    \frac{(s+c) - (s+c)(s^2-sc+c^2)}{s+c}

    The (s+c) terms cancel leaving

    1 - (1 - sc) = sc = \frac{2sc}{2}

    And now you are one identity from completing the problem.
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  3. #3
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    Apr 2010
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    thanks for the help, took me a while to understand the steps you took but I got it now. You even explained it in less steps then my teacher.
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