Question

cot 4x (sin 5x + sin 3x) = cotx (sin 5x - sin 3x)​

Answer 1

Answer

LHS :

cot4x(sin5x+sin3x)

=cot4x×2sin( 5x+3x)/2 cos( 5x-3x)/2

cos x4/sinx4 x  2 sin 4 cos x =2 cos 4 x cos x

RHS :

cotx(sin5x−sin3x)

=cotx×2sin( 5x-3x)/2 cos ( 5x-3x)/2

cos x/sinx x  2 sin cos 4 x =2 cos 4 x cos x

Thus, LHS = RHS

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