Solve a trig equation

Nov 2016
42
1
USA
Solve for x

[(2tanx)/(2+sec^2(x))] - sin^2(x) = cos^2(x)

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Also checking if the problem above may have been typed incorrectly on my worksheet. The rest of the answers on the page have been clear answers like 0,90, or 2/3 pi etc.

Here are my steps

I added sin^2(x) to the right side creating cos^2(x) + sin^2(x), which equals 1.

(2tanx)/(2+sec^2(x))] = 1

Then I substituted sec^2(x) with tan^2(x)+1.

(2tanx)/(2+tan^2(x)+1)] = 1

Simplifies to: (2tanx)/(tan^2(x) +3)] =1

Next I cross-multiplied, so 2tanx=tan^2(x) +3

After, I subtracted 2tanx, so that: tan^2(x) -2tanx +3=0

If t=tanx, then this has the form of t^2 - 2t +3. But it does not factor, and the discriminant shows there are no real solutions. Stuck.

Thank you for your assistance.
 
Last edited by a moderator:

skipjack

Forum Staff
Dec 2006
21,482
2,472
There are no real solutions, so the equation was probably mistyped.
 
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