# Trig expression simplification

Could someone explain how to simplify $\dfrac{\sin(2x)}{2-2\cos^2(x)}$? I've had tried the power reduction identity but the result did not seem much more simple. Any help would be appreciated.

• I think you should try using the identities $\sin^2x+\cos^2x=1$ and $\sin 2x=2\sin x\cos x$. – Peter Woolfitt Jun 27 '14 at 4:17

How else can you write $\sin 2x$?
$\sin 2x = 2\sin x \cos x$
How else can you write $1 - \cos^2 x$?
$1 - \cos^2 x = \sin^2 x$
$\dfrac{\sin 2x}{2 - 2 \cos^2 x} = \dfrac{\not 2 \not\sin x \cos x}{\not 2 \sin^{\not 2} x} = \boxed{\cot x}$