Prove identity : (2 cos 2x) / (cot x - tan x) = sin 2x

Step-by-step explanation:

(2 cos (2x)) / (cot x - tan x)

Multiply top and bottom by sin x cos x:

(2 cos (2x) sin x cos x) / (cos² x - sin² x)

Use double angle formula:

(2 cos (2x) sin x cos x) / (cos (2x))

2 sin x cos x

Use double angle formula:

sin (2x)