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Show that\(sin^{-1}(2x\sqrt{1-x^2})=2sin^{-1}x.\) |
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Answer» Given LHS = sin-1 (2x - √ (1 – x2)) Let x = sin θ = sin-1 (2sin θ √ (1 – sin2θ)) We know that 1 – sin2θ = cos2θ = sin-1 (2 sin θ cos θ) = sin-1 (sin2θ) = 2θ = 2 sin-1 x = RHS ∴ sin-1 (2x - √ (1 – x2)) = 2 sin-1 x |
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