Inverse Trigono...

The range of the function, $\displaystyle f\left ( x \right ) = \left ( 1 + \sec^{-1} x \right ) \left ( 1 + \cos^{-1} x \right )$ is

Number of real value of $x$ satisfying the equation, $\displaystyle \arctan \sqrt{x \left ( x+1 \right )} + \arcsin \sqrt{x \left ( x+1 \right ) + 1} = \frac{\pi}{2}$ is

The value of $x$ for which $\sin { \left( \cot ^{ -1 }{ \left( 1+x \right)  }  \right)  } =\cos { \left( \tan ^{ -1 }{ x }  \right)  }$ is:

Range of $\displaystyle f\left( x \right)=\sin ^{ -1 }{ x } +\tan ^{ -1 }{ x } +\cos ^{ -1 }{ x }$ is

$\displaystyle \alpha = \sin^{-1} \left ( \cos \left ( \sin^{-1} x \right ) \right )$ and $\displaystyle \beta = \cos^{-1} \left ( \sin \left ( \cos^{-1} x \right ) \right )$ then:

Number of value $x$ satisfying the equation $\displaystyle \sin^{-1} \left ( \frac{5}{x} \right ) + \sin^{-1} \left ( \frac{12}{x} \right ) = \frac{\pi}{2}$ is

There exists a positive real number $x$ satisfying $\displaystyle \cos \left ( \tan^{-1} x \right ) = x$. The value of $\displaystyle \cos^{-1} \left ( \frac{x^{2}}{2} \right )$ is

The greatest and least values of ${ \left( \sin ^{ -1 }{ x }  \right)  }^{ 3 }+{ \left( \cos ^{ -1 }{ x }  \right)  }^{ 3 }$ are

The value of $\sin ^{ -1 }{ \left( \sin { 10 }  \right)  }$ is

Which one of the following statement is meaningless?