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Math Help - trigo equation

  1. #1
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    trigo equation

    Would anyone please tell me how to do this?
    <br />
6tan^2 x - 4 sin^2 x =1

    Many thanks!
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  2. #2
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    Quote Originally Posted by cakeboby View Post
    Would anyone please tell me how to do this?
    <br />
6tan^2 x - 4 sin^2 x =1

    Many thanks!
    HI

    \frac{6\sin^2 x}{\cos^2 x}-4\sin^2 x-1=0

    6\sin^2 x-4\sin^2 x\cos^2 x-\cos^2 x=0

    6(1-\cos^2 x)-4(1-\cos^2 x)(\cos^2 x)-\cos^2 x=0

    6-6\cos^2 x-4\cos^2 x+4\cos^4 x-\cos^2 x=0

    Can you continue ?
    Last edited by mathaddict; December 18th 2009 at 07:13 PM.
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    HI

    \frac{6\sin^2 x}{\cos^2 x}-4\sin^2 x-1=0

    6\sin^2 x-4\sin^2 x\cos^2 x-\cos^2 x=0

    6(1-\cos^2 x)-4(1-\cos^2 x)(\cos^2 x)-\cos^2 x=0

    6-6\cos^2 x-4\cos^2 x\color{red}-\cos^4 x\color{black}-\cos^2 x=0

    Can you continue ?
    I think you need to check both the sign and the coefficient of the term in \cos^4x.

    Grandad
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  4. #4
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    Thanks for all!
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