Establish the identity: $$\frac{\sin(\alpha+\beta)}{\cos\alpha \cos\beta} = \tan\alpha+\tan\beta$$
I'm having a hard time solving this one. I changed the numerator to $\sin\alpha\cos\beta+\cos\alpha\sin\beta$ and the denominator to $\frac{1}{2}[\cos(\alpha-\beta)+\cos(\alpha+\beta)]$, but I'm not really sure what to do from there. Multiplying by the conjugate didn't seem to get me anywhere, either. I'd really appreciate help with this!