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

1. ## 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

2. Originally Posted by pederjohn
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.

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

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

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

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

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

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

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

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