Verifying Identities Pre-calculus?

Using the Reciprocal and Pythagorean Identities, verify that both sides of this equation are equal.

tanx / (1-cosx) = cscx (1+secx)

I have tried this a million different ways and I cannot get both sides to equal each other.  Is it just me?  I start off with the Left Hand Side but every time I do something, the sines and cosines end up on the top of the division sign, and not the bottom (where they are supposed to be if they are going to equal the RHS.
I'm not sure if everyone knows what verifying an equation means, but you can only work with one side of the equation at a time.  You cannot bring parts from the right-hand side over to the left-hand side.