Question

Prove it (sin 2x+sin6x)+2sin4x=4cos^2xsin4x

Answer 1

Answer:

L.H.S. = sin 2 x + 2 sin 4 x + sin 6 x

= [sin 2 x + sin 6 x ] + 2 sin 4x

= 2 sin 4 x cos 2 x + 2 sin 4x

= 2 sin 4 x cos 2 x + 2 sin 4x

= 2 sin 4 x (cos 2 x + 1)

= 2sin4x(2cos x -1+1)

= 2 sin 4 x (2 cos x )

= 4cos x sin 4 x

= R.H.S.

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