Ex 3.3, 14 - Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
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Ex 3.3, 14 Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x Taking L.H.S. sin 2x + 2sin 4x + sin 6x = (sin 6x + sin 2x) + 2sin 4x = 2 sin ((6𝑥 + 2𝑥)/2) cos ((6𝑥 − 2𝑥)/2) + 2sin 4x = 2 sin (8𝑥/2) cos (4𝑥/2) + 2sin 4x = 2 sin 4x cos 2x + 2sin 4x = 2 sin 4x (cos 2x + 1) = 2 sin 4x ( 2cos2x – 1 + 1) = 2 sin 4x (2cos2x) = 4 sin 4x cos2x = R.H.S Hence L.H.S = R.H.S Hence proved

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