If x∈(1,∞), then sin−1⁡2x1+x2 equals - Infinity Learn by Sri Chaitanya

Let $\tan^{- 1} x = θ .$ Then, $x = \tan θ$

Now,

$x \in (1, \infty) \Rightarrow \tan θ > 1 \Rightarrow \frac{π}{4} < θ < \frac{π}{2} \Rightarrow \frac{π}{2} < 2 θ < π$

$\begin{array}{l} ∴ \sin^{- 1} (\frac{2 x}{1 + x^{2}}) \\ = \sin^{- 1} (\sin 2 θ) \\ = \sin^{- 1} (\sin (π - 2 θ)) \end{array}$

$= π - 2 θ [∵ \frac{π}{4} < θ < \frac{π}{2} \Rightarrow - \frac{π}{2} < π - 2 θ < 0]$

$= π - 2 \tan^{- 1} x$

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