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Math Help - help solving a trig equation

  1. #1
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    help solving a trig equation

    hello, can anyone help me solve the problem of Tan(2x)-2sin(x)=0
    I know the double angles of tan is 2tan/1-tan^2. I get 2tan/1-tan^2 -2sin(x)=0

    I have no idea what to do from there.
    Thank you for any help given.
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  2. #2
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    Quote Originally Posted by r8654 View Post
    hello, can anyone help me solve the problem of Tan(2x)-2sin(x)=0
    I know the double angles of tan is 2tan/1-tan^2. I get 2tan/1-tan^2 -2sin(x)=0

    I have no idea what to do from there.
    Thank you for any help given.
    \tan(2x) - 2\sin{x} = 0

    \frac{\sin(2x)}{\cos(2x)} - 2\sin{x} = 0

    \frac{2\sin{x}\cos{x}}{\cos(2x)} - 2\sin{x} = 0

    2\sin{x}\left[\frac{\cos{x}}{\cos(2x)} - 1\right] = 0<br />

    2\sin{x}\left[\frac{\cos{x} - \cos(2x)}{\cos(2x)}\right] = 0

    2\sin{x}\left[\frac{1 + \cos{x} - 2\cos^2{x}}{\cos(2x)}\right] = 0<br />

    2\sin{x}\left[\frac{(1+2\cos{x})(1-\cos{x})}{\cos(2x)}\right] = 0

    \sin{x} = 0

    \cos{x} = -\frac{1}{2}

    \cos{x} = 1

    finish up ?
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  3. #3
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    yes thank you. The double angles always get me.
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