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