Prove the identity with steps. sin (x-y) / cos x sin y = tan x cot y - 1

Step-by-step explanation:

sin (x-y) / (cos x sin y)

Use angle sum/difference formula:

(sin x cos y - sin y cos x) / (cos x sin y)

Divide:

(sin x cos y) / (cos x sin y) - 1

Rearrange:

(sin x / cos x) (cos y / sin y) - 1

Simplify:

tan x cot y - 1