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Prove that Sin 2x + 2sin 4x + Sin 6x = 4cos2 X Sin 4x - Mathematics

Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x

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Solution

L.H.S. = sin 2x + 2 sin 4x + sin 6x

= [sin 2x + sin 6x] + 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)

= 4cos2 x sin 4x

= R.H.S.

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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 3 Trigonometric Functions
Q 14 | Page 73
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