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Show that sin-1( 2x \(\sqrt{1-x^2}\) ) = 2 sin-1 x. |
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Answer» Given LHS = sin-1 (2x - √ (1 – x2)) Let x = sin θ = sin-1 (2sin θ √ (1 – sin2 θ)) We know that 1 – sin2 θ = cos2 θ = sin-1 (2 sin θ cos θ) = sin-1 (sin2 θ) = 2θ = 2 sin-1 x = RHS ∴ sin-1 (2x - √ (1 – x2)) = 2 sin-1 x |
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