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?