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Math Help - Show the the equaton 2tan^2xcosx=3 can be written in the form 2cos^2x+3cosx-2=0

  1. #1
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    Show the the equaton 2tan^2xcosx=3 can be written in the form 2cos^2x+3cosx-2=0

    Can someone help me to solve this equation

    They ask Show that the equation 2tan^2xcosx=3 can be written in the form 2cos^2x+3cos-2=0

    I got it right so far to make everything cos but not without the ^2

    here is what i did:

    2tan^2xcosx =3
    ---------------------------------------------------------------------------------
    2sin^2x
    ---------- cosx = 3
    2cos^2x
    ---------------------------------------------------------------------------------
    2-2cos^2x
    ------------
    2cos^2
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by pederjohn View Post
    Can someone help me to solve this equation

    They ask Show that the equation 2tan^2xcosx=3 can be written in the form 2cos^2x+3cos-2=0

    I got it right so far to make everything cos but not without the ^2

    here is what i did:

    2tan^2xcosx =3
    ---------------------------------------------------------------------------------
    2sin^2x
    ---------- cosx = 3
    2cos^2x
    ---------------------------------------------------------------------------------
    2-2cos^2x
    ------------
    2cos^2
    Hi pederjohn,

    Just use a few simple identities and you're there.

    2 \tan^2x \cos x=3 \Longleftrightarrow \boxed{2 \cos^2x + 3\cos x-2=0}

    2\left(\frac{\sin^2 x}{\cos^2 x}\right)\cos x=3

    \frac{2\sin^2x}{\cos x}=3

    2 \sin^2x-3 \cos x=0

    2(1-\cos^2 x)-3 \cos x=0

    2-2 \cos^2x-3 \cos x=0

    \boxed{2 \cos^2 x+3 \cos x -2 =0}
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