Prove that sin2x 2sin4x sin6x 4 cos 2x sin 4x
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Prove that sin 2x + 2sin 4x + sin 6x = 4cos^2x sin4x
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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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