Prove that sin2x + 2 sin4x + sin6x = 4 cos^2 x sin4x
Prove that sin2x + 2 sin4x + sin6x = 4 cos2 x sin4x
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sin 2x= sin (4x-2x) = sin 4x cos 2x - cos 4x sin 2x
sin 4x = sin 4x
sin 6x = sin (4x+2x) = sin 4x cos 2x + cos 4x sin 2x
Adding we get:
= sin 2x + 2 sin 4x + sin 6x
= 2 sin 4x cos 2x + 2sin 4x
= 2 sin 4x( cos 2x + 1)
= 2 sin 4x ( 2 cos2 x)
= 4 sin 4x cos2 x
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