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    Trigonometry Question: Double of Half Angle Formula

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    Use a double or half angle formula to solve the equation in the interval [0, 2x].
    a) tan (x/2) - sin(x) = 0
    b) tan(x) + cot(x) = 4sin(2x)

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    https://brainmass.com/math/trigonometry/trigonometry-question-double-half-angle-formula-512753

    Solution Preview

    tan x/2 = sin x
    sin x/2/ cos x/2 = 2 sin x/2 cos x/2

    sin x/2 = 0 or 1/ cos x/2 = 2 cos x/2
    cos^2 (x/2) = ½

    Case 1.
    sin x/2 = 0
    x/2 = npie
    x = +/- 2npie => x = 0, 2pie (these are the solutions within the given interval of x)

    Case 2.
    cos x/2 = 1/?2
    x/2 = pie/4 and 2pie - pie/4 = 7pie/4 are solutions. (1st and 4th quadrants)
    x/2 = pie/4 + 2npie and ...

    Solution Summary

    In this solution we solve two trigonometry questions using a double or half angle formula.

    $2.49

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