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 cos^{2} x)

= 4 sin 4x cos^{2} x