I can't seem to figure this out...

tanx/cscx=secx-cosx

It almost always works best if you substitute sines and cosines for the tangent, cosecant etc.

The left hand side is:

tanx/cscx = (sinx/cosx)*(sinx/1) = sin^2x/cosx

The right hand side is:

secx - cosx = 1/cosx - cosx = 1/cosx - cos^2x/cosx = (1 - cos^2x)/cosx

Can you take it from here?

Yes thanks