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Math Help - Solving a cosine integral

  1. #1
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    Solving a cosine integral

    I have to following problem:



    Given that:





    The problem is that i do not see the step between:



    and:



    I tried rewriting to cosine functions but that only got me deeper in to trouble leaving me with cot functions and i don't think that is what i want to get here.

    I hope some one could me help me out, thanks in advance
    Attached Thumbnails Attached Thumbnails Solving a cosine integral-screen-shot-2011-01-07-1.23.27-am.png   Solving a cosine integral-screen-shot-2011-01-07-1.17.45-am.png   Solving a cosine integral-screen-shot-2011-01-07-1.22.55-am.png   Solving a cosine integral-screen-shot-2011-01-07-1.28.21-am.png  
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  2. #2
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    Split the integral into two:

    \begin{aligned} \displaystyle \int_{0}^{\pi}\frac{A_{1}\cos{\theta}+A_{3}\cos{3\  theta}}{\cos{\theta}-\cos{\theta_{0}}}\;{d{\theta}}& = \int_{0}^{\pi}\frac{A_{1}\cos{\theta}}{\cos{\theta  }-\cos{\theta_{0}}}\;{d\theta}+\int_{0}^{\pi}\frac{3  A_{3}\cos{3\theta}}{\cos{\theta}-\cos{\theta_{0}}}\;{d\theta} \\& = A_{1}\int_{0}^{\pi}\frac{\cos{\theta}}{\cos{\theta  }-\cos{\theta_{0}}}\;{d\theta}+3A_{3}\int_{0}^{\pi}\  frac{\cos{3\theta}}{\cos{\theta}-\cos{\theta_{0}}}\;{d\theta}. \end{aligned}
    Last edited by TheCoffeeMachine; January 6th 2011 at 04:49 PM.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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