Prove this Trig Identity? (cosx/secx) - (sinx/cotx) = (cosxcotx-tanx)/(cscx) thanks in advance!

I usually find it easier to do these if I express everything in terms of sinx or cosx.
  secx = 1/cosx
  cotx = cosx/sinx
  tanx = sinx/cosx
  cscx = 1/sinx
So, we can rewrite the question as
  (cosx/(1/cosx)) - (sinx/(cosx/sinx)) = (cosx*(cosx/sinx)-sinx/cosx)/(1/sinx)
  because(x)^2 - sin(x)^2/cosx = (because(x)^2/sinx - sinx/cosx)*sinx    (simplify a bit)
  because(x)^3 - sin(x)^2 = because(x)^3 - sin(x)^2    (multiply by cosx)