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Thread: Theorem

  1. #1
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    Theorem

    Use Theorem s(x+y)= s(x)c(y)+c(x)s(y) to show

    cos(4x)=

    Then apply this formula to find the value of cos(/8)
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Theorem

    $\displaystyle \cos(4x)=\cos(2(2x))=1-2\sin^2(2x)=1-2(\sin(x+x))^2$

    Now apply the angle-sum identity for sine as required.

    Then use:

    $\displaystyle x=\frac{\pi}{8}$ in the resulting formula. I would suggest letting $\displaystyle u=\cos^2(x)$ to get a quadratic in $\displaystyle u$. Take the appropriate root.
    Last edited by MarkFL; Nov 13th 2012 at 09:00 PM.
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