Trig Identity Proofs I'm having a really hard time understanding how to do these. The directions are to verify that each of the following is an identity:
$$\dfrac{\csc x}{\cot x+\tan x}=\cos x$$ 
I have to get the left side to equal the right. 

$$ \frac{ \csc x }{ \cot x + \tan x} = \frac{\frac{1}{\sin x}}{\frac{\cos x}{\sin x} + \frac{ \sin x}{ \cos x}} = \frac{\frac{1}{\sin x}}{\frac{ \cos^2 x + \sin^2 x}{\sin x \cos x}} = \frac{ \frac{1}{\sin x}}{\frac{1}{\cos x \sin x}} = \frac{ \cos x \sin x}{\sin x} = \cos x$$
I have used the identiy $\sin^2 x + \cos^2 x = 1 $
