Solved :secx + tanx = 1/(secx-tanx)

Could someone please help me prove the following identity.

I got as far as this starting with the R.H.S, but don't know if it's the right approach or how to proceed from here.

Any help would be much appreciated, thank you.

**Now solved**. I multiplied the denominator and numerator by , then it was easy.

Re: secx + tanx = 1/(secx-tanx)

You are correct, now just write it as 1/[(1-sinx)/cosx] and proceed further.

Alternatively multiply and divide the numerator and denominator by ( secx-tanx) the numerator will reduce to 1 and you will get the RHS.

Re: secx + tanx = 1/(secx-tanx)

Thank you very much for your reply, sorry I did not say in my original post, but I actually started with the R.H.S. I've now edited my post accordingly thank you.