cotx = cosx/sinx
cscx = 1/sinx
If we plug these into your equation we get:
(cosx/sinx)/(1/sinx) - 1
Dividing by a number is the same as multiplying by its reciprocal so it can be rewritten as:
(cosx/sinx)(sinx) - 1
The two sinx's cancel each other out so we end up with cosx - 1