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Ex 3.3, 12 - Prove that sin2 6x - sin2 4x = sin⁡2x sin⁡10x - (x + y) formula

Ex 3.3, 12 - Chapter 3 Class 11 Trigonometric Functions - Part 2

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Ex 3.3, 12 Prove that sin2 6 sin2 4 = sin 2 sin 10 Solving L.H.S. sin2 6x sin2 4x Using a2 b2 = (a + b) (a - b) = (sin 6x + sin 4x) (sin 6x sin 4x) Lets calculate (sin 6x + sin 4x) and (sin 6x sin 4x) separately Hence sin2 6x sin2 4x = (sin 6x + sin 4x) (sin 6x sin 4x) = (2 sin 5x cos x) (2 cos 5x sin x) = (2 sin 5x cos 5x) . (2 sin x cos x) = (sin 10x) (sin 2x) = R.H.S. Hence, L.H.S. = R.H.S. Hence proved

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