If x∈(1,∞), then sin−1⁡2×1+x2 equals

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

1. A

2. B

3. C

4. D

none of these

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### Solution:

Let ${\mathrm{tan}}^{-1}x=\theta \text{.}$ Then, $x=\mathrm{tan}\theta$

Now,

$x\in \left(1,\mathrm{\infty }\right)⇒\mathrm{tan}\theta >1⇒\frac{\pi }{4}<\theta <\frac{\pi }{2}⇒\frac{\pi }{2}<2\theta <\pi$

$=\pi -2{\mathrm{tan}}^{-1}x$

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