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Math Help - Identity proof

  1. #1
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    Identity proof

    Hello,

    I am having trouble simplifying this identity [cos4x= 2cos^2 2x-1]. I thought I could solve it with the double angle identity, but the 2x seems to be getting in the way. Can I remove the 2x and multiply it by the identity cos2x?
    Last edited by Sedgewick19; May 18th 2010 at 03:09 PM. Reason: misspell
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Sedgewick19 View Post

    Hello,


    I am having trouble proving this identity [cos4x= 2cos^2 2x-1]. I thought I could solve it with the double angle identity, but the 2x seems to be getting in the way. Can I remove the 2x and multiply it by the identity cos2x?
    It's just a simple substitution really...

    \cos(2x)= 2\cos^2(x)-1 you know.

    Well in the 4x case, just set y = 2x.

    Then you have \cos(4x) = \cos(2y) = 2\cos^2(y)-1 = 2\cos^2(2x) - 1
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  3. #3
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    Thanks, I thought that may have been the way the solve the problem, but I was afraid that it was too easy.
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