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Math Help - reduction formula

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    83

    reduction formula

    i have shown

    if

     <br />
I_n=\int \frac {sin (2n\theta)}{sin \theta}<br />
    then

     <br />
I_n=I_{n-1}+ \frac {2}{2n-1} sin (2n-1)\theta<br />


    the next part is hence,find

     <br />
I_n=\int ^{\frac{\pi}{2}}_0 \frac {sin (5\theta)}{sin \theta}<br />

    Im missing something here. I split sin(5\theta) as sin(4\theta+\theta) etc
    but all this does is evaluate the integral in terms of a reduction formula, not using part (a)
    What is the trick i am missing to use part (a) and not just evaluate the second integral?
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  2. #2
    Member
    Joined
    Dec 2009
    Posts
    83
    A few questions on and i have to prove a reduction formulae for sin (nx)/sin x

    which will kill my problem. But i am still at loss of how to do it with the formula i have derived in part(a)
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