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Euler's formula proof help

  1. Feb 7, 2006 #1
    Hi. I am trying to prove that (2sin^4x(2cos^2x+1))/3 = [sin^2(2x)/6-1/3][cos(2x)].

    I tried fixing the right side, changing cos2x to 1 - 2sin^2x, and I went all the way to

    (4sin^2x-4sin^4x-2-8sin^4x+8sin^6x+4sin^2x)/6.

    I am clueless on how to continue the proof. Please help. Thanks.
     
  2. jcsd
  3. Feb 8, 2006 #2

    Tide

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    Homework Helper

    Your notation isn't very clear but I think this may help:

    [tex]e^{4 i \theta} = \left( e^{i \theta} \right)^4[/tex]

    and apply Euler's formula to the individual exponentials.
     
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