There can be easier solutions to the problem than the way I do it, but usually it works out not too bad.

I always replace things like cot(A) and cosec(A) (and whatever else) with sines and cosines. So for your identity we have

Generally the next step is to add fractions. So we have fractions...let's add them. The common denominator will simply be

So what's the LHS look like?

-Dan