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

**pederjohn** · April 29th 2010, 02:32 AM

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

**masters** · April 29th 2010, 04:28 AM

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.

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

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

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

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

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

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

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

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

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