How to prove :

I think what you meant to ask was this:


\frac {sec \theta}{1 + \cos\theta} = csc^2 \theta (sec \theta -1)


The first thing to do is change the secant and cosecant functions into their sine and cosine equivalents. Then you should see that if you multiply both sides by the same factors in order to get rid of the denominators it will fall right out.

Here is some hint:
\sin^2\theta=1-\cos^2\theta=(1-\cos\theta)(1+\cos\theta)
= \cos\theta (\sec\theta -1)(\cos\theta+1)

Can you continue from this point?