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Math Help - Solve the trigonometric equation?

  1. #1
    Super Member fardeen_gen's Avatar
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    Solve the trigonometric equation?

    Solve the equation for x:
    \left(\frac{1 - a\sin x}{1 + a\sin x}\right)\sqrt{\frac{1 + 2a\sin x}{1 - 2a\sin x}} = 1,\ a\in\mathbb{R}
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  2. #2
    MHF Contributor
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    Quote Originally Posted by fardeen_gen View Post
    Solve the equation for x:
    \left(\frac{1 - a\sin x}{1 + a\sin x}\right)\sqrt{\frac{1 + 2a\sin x}{1 - 2a\sin x}} = 1,\ a\in\mathbb{R}
    Hi

    \frac{1 + 2a\sin x}{1 - 2a\sin x} = \frac{(1 + a\sin x)^2}{(1 - a\sin x)^2},\ a\in\mathbb{R}

    (1 + 2a\sin x)(1 - a\sin x)^2 = (1 + a\sin x)^2(1 - 2a\sin x),\ a\in\mathbb{R}

    Expand and simplify
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