# The value of tan–1 2 2 2 2 1x 1x 1x 1x é ù + +- ê ú ë û + — , 1 |x| ,x 0 2 < ¹ , is equal to

Question:

The value of $\tan ^{-1}\left[\frac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right],|x|<\frac{1}{2}, x \neq 0$, is equal to

1. $\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} \mathrm{x}^{2}$

2. $\frac{\pi}{4}+\cos ^{-1} x^{2}$

3. $\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} \mathrm{x}^{2}$

4. $\frac{\pi}{4}-\cos ^{-1} \mathrm{x}^{2}$

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Online April 8, 2017

Solution:

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