Question

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

Answer 1

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