The equation \({\tan ^{ - 1}}\left( {1 + {\rm{x}}} \right) + {\tan ^{ - 1}}\left( {1 - {\rm{x}}} \right) = \frac{{\rm{\pi }}}{2}\) is satisfied by

The equation \(sin^{-1}x-cos^{-1}x=\frac{\pi}{6}\) has

What is \(\tan \left\{ 2{{\tan }^{-1}}\left( \frac{1}{3} \right) \right\}\) equal to?

What is the value of \({\sin ^{ - 1}}\frac{4}{5} + {\sec ^{ - 1}}\frac{5}{4} - \frac{\pi }{2}?\)

If \({\sin ^{ - 1}}\frac{{2p}}{{1 + p2}} - {\cos ^{ - 1}}\frac{{1 - {q^2}}}{{1 + {q^2}}} = {\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}}\) , then what is x equal to?

Consider the following values of x:

1) 8

2) -4

3)  \(\frac 16\)

4)  \(- \frac{1}{4}\)

Which of the above values of x is/are the solution(s) of the equation

\({\tan ^{ - 1}}\left( {2x} \right) + {\tan ^{ - 1}}\left( {3x} \right) = \frac{\pi }{4}?{\rm{\;}}\)

What is \(\tan ^{- 1}\left( {\frac{1}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{3}{5}} \right)\) equal to?

Let the equation sec x.cosec x = p have a solution, where p is a positive real number. What should be the smallest value of p?

The imaginary part of log sin (x + iy) is:

The value of \({\tan ^{ - 1}}\left( {\frac{1}{2}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{3}} \right)\) is

The function \(f(x) = \sqrt {\cos (\sin x)} + {\sin ^{ - 1}}\left( {\frac{{1 + {x^2}}}{{2x}}} \right)\) is defined for

The value of \({\cos ^{ - 1}}\left( {\cos \frac{{5\pi }}{3}} \right) + {\sin ^{ - 1}}\left( {\sin \frac{{5\pi }}{3}} \right)\) is