# Math Help - Proving an identity.

1. ## Proving an identity.

Hey guys!

I'm stuck on a proof:

$\frac{sin x}{1-cot x}-\frac{cos x}{tan x - 1} = sin x + cos x$

I hate to be the kind of person who just dumps a problem on a forum without any work done, but proofs are kind of a special thing. It's like either you know where to start, or you don't.

In this case, I don't!

Thanks for any help.

2. Hi

$\frac{\sin x}{1-\cot x}-\frac{\cos x}{\tan x - 1} = \frac{\sin x}{1-\frac{\cos x}{\sin x}}-\frac{\cos x}{\frac{\sin x}{\cos x} - 1} = \frac{\sin^2 x}{\sin x - \cos x}-\frac{\cos^2 x}{\sin x - \cos x}$

$\frac{\sin x}{1-\cot x}-\frac{\cos x}{\tan x - 1} = \frac{\sin^2 x - \cos^2 x}{\sin x - \cos x} = \sin x + \cos x$

3. Thank you, running-gag!