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Math Help - Problem with half angle question

  1. #1
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    Problem with half angle question

    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
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  2. #2
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    Hello offahengaway and chips
    Quote Originally Posted by offahengaway and chips View Post
    sin^4Θ=3/8 - 1/2cos(2Θ) + 1/8 cos(4Θ)
    \sin^4\theta = (1-\cos^2\theta)^2

    =\Big(1 - \tfrac12(1+\cos 2\theta)\Big)^2

    =(\tfrac12-\tfrac12\cos 2\theta)^2

    =\tfrac14-\tfrac12\cos 2\theta +\tfrac14\cos^22\theta

    = \tfrac14 -\tfrac12\cos 2\theta +\tfrac14\cdot\tfrac12(\cos 4\theta+1)

    = \tfrac38 - \tfrac12\cos 2\theta +\tfrac18\cos 4\theta

    Grandad
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