cot 4x(sin 5x + sin 3x) = cot x(sin 5x - sin 3x)
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taking LHS
= Cot 4x (2 sin 5x+3x/2 × cos5x-3x/2)
= cot 4x (2 sin4x cosx)
= cos 4x/sin4x ×2 sin4x cosx
= 2cos4x cosx
taking RHS
= cotx (2 cos 5x+3x/2 sin 5x-3x/2)
= cotx (2 cos4x sinx )
= cosx/sinx ×2 cos4x sinx
= 2 cos4x cosx
Hence,
LHS = RHS
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