Question

Prove that : Cot 4x (Sin 5x +Sin 3x) = Cot x (Sin 5x - Sin 3x)

Answer 1

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Check this attachment.

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Answer 2

L.H.S

cot4x(sin5x+sin3x)

⇒cot4x×2sin5x+3x2.cos5x−3x2

⇒cotx×2sin4x.cosx

⇒cos4xsin4x×2sin4x.cosx

⇒2cos4xcosx×sinxsinx

⇒cosxsinx2cos4xsinx

⇒cotx(sin(4x+x)−sin(4x−x))

⇒cotx(sin5x−sin3x)=R.H.S

Hence proved.

HOPE IT HELPS ✌