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Math Help - Half angle formula problem

  1. #1
    Junior Member
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    Half angle formula problem

    Having trouble applying half angle formula in this question,

    Any hints would be great

    sin^4Θ=3/8 - 1/2cos(2Θ) + 1/8 cos(4Θ) is a solution for any angle Θ

    use half angle formula and cos^2(2Θ)=1/2 cos(4Θ) +1/2

    thanks

    p.s just moved this, posted it in geometry by accident
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  2. #2
    MHF Contributor red_dog's Avatar
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    \sin^4\theta=(\sin^2\theta)^2=\left(\frac{1-\cos 2\theta}{2}\right)^2=

    =\frac{1}{4}(1-2\cos 2\theta+\cos^2 2\theta)=

    =\frac{1}{4}\left(1-2\cos 2\theta+\frac{1+\cos 4\theta}{2}\right)=

    =\frac{1}{4}-\frac{1}{2}\cos 2\theta+\frac{1}{8}+\frac{1}{8}\cos 4\theta=

    =\frac{3}{8}-\frac{1}{2}\cos 2\theta+\frac{1}{8}\cos 4\theta
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