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Thread: Help with using half angle identity/formula

  1. #1
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    Help with using half angle identity/formula

    Help with using half angle identity/formula-please-help.png
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: Help with using half angle identity/formula

    $\sin^2(x) = \frac{1}{2} \left( 1 - \cos 2x\right)$

    Hence $\sin^4 2x = (\sin^2 2x)^2 = \left(\frac{1}{2}(1-\cos 4x)\right)^2 $ expand and use the identity $\cos^2 y = \frac{1}{2} ( 1 + \cos 2y)$ to get $\cos 8x$
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  3. #3
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    Re: Help with using half angle identity/formula

    Quote Originally Posted by Amer View Post
    $\sin^2(x) = \frac{1}{2} \left( 1 - \cos 2x\right)$

    Hence $\sin^4 2x = (\sin^2 2x)^2 = \left(\frac{1}{2}(1-\cos 4x)\right)^2 $ expand and use the identity $\cos^2 y = \frac{1}{2} ( 1 + \cos 2y)$ to get $\cos 8x$
    So what value would I input into the red box?
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