I need to show working and prove that: (cosx)/(1-sinx) + (cosx)/(1+sinx) = 2Secx

What seems to be the trouble?

You have:

\frac{cosx}{1-sinx}+\frac{cosx}{1+sinx}

Now, the objective is to show that it is equal to 2secx.

As with any fraction, get the denominators the same. What's your LCD?:

It's (1+sinx)(1-sinx)

\frac{(1+sinx)cosx}{(1+sinx)(1-sinx)}+\frac{cosx(1-sinx)}{(1+sinx)(1-sinx)}

Now, finish up? Remember that 1-sin^{2}x=cos^{2}x

Thanks for your help