# Trig identities solve for $\frac1{2} \tan(x)$

How to prove

$$\frac{\sin^2(x)}{1+\cos(2x)} = \frac1{2} \tan^2(x)$$

-
please do not ask question in imperative mode. – user5501 Apr 20 '11 at 16:38
I have downvoted, so I feel obligated to explain my motives. 1) You have not shown your work, nor indicated that you tried to solve it. 2) Question is asked in imperative mode. 3) Question is ambiguously formatted. 4) By showing no work or interest (except for an answer) at question of this level, I think it is on verge of being too localized. If you address the above points, I would be more than glad to retract my downvote. – user5501 Apr 20 '11 at 16:55
Dude please accept an answer. – user9413 Apr 23 '11 at 11:27

Hint: $1+ \cos{2x} = 1 + 2\cos^{2}{x} -1 = 2\cos^{2}{x}$
Hint: use the Pythagorean trigonometric identity $\sin^2 x+\cos^2 x=1$ and the double-angle formula $\cos 2x=\cos^2 x-\sin^2 x$
Do you know the addition formula $\cos(a+b)=\cos (a)\cos b−\sin (a)\sin (b)$ ? For $a=b=x$ yields $\cos(2x)=\cos^2 (x)−\sin^2 (x)$. Then insert this result into your identity.