The simplest form of $${\tan ^{ - 1}}\left[ {{{\sqrt {1 + x} - \sqrt {1 - x} } \over {\sqrt {1 + x} + \sqrt {1 - x} }}} \right]$$ is

If for the matrix $$A = \left[ {\matrix{ \alpha & { - 2} \cr { - 2} & \alpha \cr } } \right]$$, | A³ | = 125, then the value of $$\alpha$$ is

If $$y = \sin (m{\sin ^{ - 1}}x)$$, then which one of the following equations is true?

The principal value of $$[{\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )]$$ is