We have, L.H.S. = cot 4x (sin 5x + sin 3x) = cot 4x × 2 sin $\left(\frac{5x+3x}{2}\right)$ cos $\left(\frac{5x-3x}{2}\right)$ = $\frac{\cos 4x}{\sin 4x}$ × 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 $\left(\frac{5x-3x}{2}\right)$ cos $\left(\frac{5x+3x}{2}\right)$ = $\frac{\cos x}{\sin x}$ × 2 sin x cos 4x = 2 cos 4x cos x ... (ii) From (i) & (ii), we get L.H.S.= R.H.S.