I have a major problem with verifying a Trigonometric identity. (My teacher couldn't really get it, so I would like to find it just in case it appears on a test)
The problem goes like this:
$\sin(\theta) + \cos(\theta) = \frac{\sin(\theta)}{1 - \cot(\theta)} + \frac{\cos(\theta)}{1 - \tan(\theta)}$
Where I must verify that this is true. I have tried numerous operations, mostly getting to $\sin + \cos$ along with a crazy fraction in the numerator and another fraction in the numerator. As I have said, my teacher showed my something, but it really did not work after I continued simplifying.
If there is anyone who would help guide me in this, it would be much appreciated.