Question

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

Answer 1

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.

Answer 2

heya.....
the solution is in the pic

hope it helps u
^_^