Prove that: 

To prove:  sin 2x + 2 sin 4x + sin 6x = 4 cos²x sin 4x
Formula to use: 

Proof: 

L.H.S = sin 2x + 2 sin 4x + sin 6x

L.H.S = 2 sin 4x + (sin 6x + sin 2x)

We know,

L.H.S = 2 sin 4x + 2 sin 4x cos 2x

Taking 2 sin 4x common from the equation,

= 2 sin 4x × (1 + cos 2x)

= 2 sin 4x × 2 cos² x                         [∵ cos2x = 2cos² x – 1]

L.H.S = 4 cos² x sin 4x
R.H.S = 4 cos² x sin 4x

∴ L.H.S = R.H.S

Hence, proved.