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    Working with half-angle identity

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    Cos x (using the half-angle identity)

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/working-half-angle-identity-13879

    SOLUTION This solution is FREE courtesy of BrainMass!

    We have the half angle identity for cos x as,
    cos x = +-sqrt[(1 + cos 2x)/2]

    also, cos 7pi/12 = cos 105 = cos (210/2)

    so, cos 105 = -sqrt[(1 + cos 210)/2]
    (since 105 degrees is in quadrant II and cos is negative there)

    Therefore,
    cos 105 = -sqrt[(1 + cos{2*90 + 30})/2]
    = -sqrt[(1 + -cos 30)/2]
    = -sqrt[(1 - (sqrt3)/2)/2] (cos 30 = [sqrt3]/2)
    = -sqrt[{2 - sqrt3}/4]
    = -0.25881

    which is the required value

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf>
    https://brainmass.com/math/geometry-and-topology/working-half-angle-identity-13879

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