Question

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

Answer 1

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LHS :

cot4x(sin5x+sin3x)

=cot4x×2sin(25x+3x)cos(25x−3x)

=sin4xcos4x×2sin4xcosx=2cos4xcosx

RHS :

cotx(sin5x−sin3x)

=cotx×2sin(25x−3x)cos(25x+3x)

=sinxcosx×2sinxcos4x=2cos4xcosx

Thus, LHS = RHS