Q. 144.2( 115 Votes )

Prove that: 

Answer :

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.

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