We have, L.H.S. = cos (

3π

2

+x) cos (2π + x) [cot(

3π

2

−x)+cot(2π+x)]
= (sin x) (cos x) [tan x + cot x]
Since cos (

3π

2

+x) = sinx , cos (2π + x) = cos x , cot (

3π

2

−x) = tan x , cot (2π + x) = cot x
= cos x sin x [

sin2x+cos2x

cosxsinx

] = 1 = R.H.S.