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Math Help - Identity

  1. #1
    Super Member dhiab's Avatar
    Joined
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    ALGERIA
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    Identity

    Prove the identity :
     <br />
(\frac{1}{2}+\cos \frac{\pi }{20})(\frac{1}{2}+\cos \frac{3\pi }{20})(\frac{1}{2}+\cos \frac{9\pi }{20})(\frac{1}{2}+\cos \frac{27\pi }{20})=\frac{1}{16}<br />
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  2. #2
    Member
    Joined
    Sep 2009
    Posts
    82

    wow

    I expanded the left side of equation with a program, so this should be correct. From here I am sorry to say I cannot help. I thought there would be more simplification, but I do not see anything helpful.
    \dfrac{1}{16}+1/8cos(\dfrac{\pi}{20})+1/8cos(\dfrac{3\pi}{20})+1/4cos(\dfrac{\pi}{20}) cos(\dfrac{3\pi}{20})+1/8sin(\dfrac{\pi}{20})+1/4cos(\dfrac{\pi}{20})sin(\dfrac{\pi}{20}) +1/4cos(\dfrac{3\pi}{20})sin(\dfrac{\pi}{20})+1/2cos(\dfrac{\pi}{20}) cos(\dfrac{3\pi}{20})sin(\dfrac{\pi}{20})-1/8sin(\dfrac{3\pi}{20}) -1/4cos(\dfrac{\pi}{20})sin(\dfrac{3\pi}{20})-1/4cos(\dfrac{3\pi}{20})sin(\dfrac{3\pi}{20})-1/2cos(\dfrac{\pi}{20}) cos(\dfrac{3\pi}{20})sin(\dfrac{3\pi}{20})-1/4sin(\dfrac{\pi}{20})sin(\dfrac{3\pi}{20})-1/2cos(\dfrac{\pi}{20})sin(\dfrac{\pi}{20}) sin(\dfrac{3\pi}{20})-1/2cos(\dfrac{3\pi}{20})sin(\dfrac{\pi}{20}) sin(\dfrac{3\pi}{20})-cos(\dfrac{\pi}{20})cos(\dfrac{3\pi}{20})sin(\dfra  c{\pi}{20})sin(\dfrac{3\pi}{20})

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