Hi there!
L.H.S. = sin 2x + 2 sin 4x + sin 6x
= sin 2x + sin 6x + 2 sin 4x
= 2 sin [tex]\dfrac {2x + 6x}{2}[/tex] . cos [tex]\dfrac {2x - 6x}{2}[/tex] + 2 sin 4x
= 2 sin 4x . cos (-2x) + 2 sin 4x
= 2 sin 4x . cos 2x + 2 sin 4x
= 2 sin 4x (cos 2x + 1)
= 2 sin 4x (2 cos² x - 1 + 1)
= 2 sin 4x (2 cos² x) = 4 sin 4x . cos² x = R.H.S.
HENCE PROVED.
~ Hope it helps!
