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Math Help - Prove this identity

  1. #1
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    Prove this identity

    Can anyone help me prove this trig identity:

    Cos(4ά)+4cos(2ά)+3=8cos(4ά)

    Thanks
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  2. #2
    A Plied Mathematician
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    I think the identity is

    \cos(4\alpha)+4\cos(2\alpha)+3=8\cos^{4}(\alpha), right?
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  3. #3
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    Yes, thats right. Sorry...

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  4. #4
    A Plied Mathematician
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    Ok. So what ideas have you had so far?
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  5. #5
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    [IMG]URL=http://img263.imageshack.us/i/64044892.png/]

    Thats what I did...I try everything...still nothing
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  6. #6
    A Plied Mathematician
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    Two comments:

    1. \cos(4\alpha)=\cos^{4}(\alpha)-2\sin^{2}(\alpha)\cos^{2}(\alpha)+\sin^{4}(\alpha)-4\sin^{2}(\alpha)\cos^{2}(\alpha).

    You missed some squares in there.

    2. In your expression, you still have a \cos(2\alpha) in there. Reduce the angle, and see what you get.
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