We have, L.H.S. = cot 4x (sin 5x + sin 3x)
= cot 4x × 2 sin (

5x+3x

2

) cos (

5x−3x

2

)
=

cos4x

sin4x

× 2 sin 4x cos x = 2 cos 4x cos x ... (i)
And, R.H.S.= cot x (sin 5x – sin 3x)
= cot x × 2 sin (

5x−3x

2

) cos (

5x+3x

2

)
=

cosx

sinx

× 2 sin x cos 4x = 2 cos 4x cos x ... (ii)
From (i) & (ii), we get L.H.S.= R.H.S.