If x∈(1$$,∞$$), then $$sin$$−$$1$$⁡$$2x1+x2$$ equals

Correct option is 4none of these

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If $x \in (1, \infty),$ then $\sin^{- 1} (\frac{2 x}{1 + x^{2}})$ equals

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2 tan−1⁡x

π -2 tan−1⁡x

-π -2 tan−1⁡x

none of these

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detailed solution

Correct option is D

Let tan−1⁡x=θ. Then, x=tan⁡θNow, x∈(1,∞)⇒tan⁡θ>1⇒π4<θ<π2⇒π2<2θ<π∴ sin−1⁡2x1+x2 = sin−1⁡(sin⁡2θ) = sin−1⁡(sin⁡(π−2θ)) = π−2θ ∵π4<θ<π2⇒−π2<π−2θ<0 =π−2tan−1⁡x

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If x∈(1,∞), then sin−1⁡2x1+x2 equals

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If $x \in (1, \infty),$ then $\sin^{- 1} (\frac{2 x}{1 + x^{2}})$ equals