JEE Math Practice Question

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

1. A.$${\pi \over 4} + {1 \over 2}{\cos ^{ - 1}}\,{x^2}$$
2. B.$${\pi \over 4} + {\cos ^{ - 1}}\,{x^2}$$
3. C.$${\pi \over 4} - {1 \over 2}{\cos ^{ - 1}}\,{x^2}$$
4. D.$${\pi \over 4} - {\cos ^{ - 1}}\,{x^2}$$