# Prove that cot4x (sin5x + sin3x) = cot x (sin5x – sin3x)

To prove cot4x (sin5x + sin3x) = cot x (sin5x – sin3x)

LHS = cot 4x (sin 5x + sin 3x)

We know,  LHS = cot 4x × 2 sin 4x × cos x LHS = 2 cos 4x cos x

RHS = cot x (sin 5x – sin 3x)

We know,  RHS = cot x × 2 cos 4x × sin x RHS = 2 cos 4x cos x

LHS = RHS

Hence, proved

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