Question

Identify the expression that is equivalent to cot x/ csc x -1

Answer 1

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