Find the principal value of $\tan ^{-1}(-1)$.

$\cos \left(\tan^{-1} x\right) = . . . . . . . (|x| < 1)$.

If $x$ is a real number,then the number of solutions of $\operatorname{Tan}^{-1}(\sqrt{x(x+1)})+\operatorname{Sin}^{-1}(\sqrt{x^2+x+1})=\frac{\pi}{2}$ is:

If $\lim _{x \rightarrow 0} \frac{\sin ^{-1} x - \tan ^{-1} x}{3 x^{3}}$ is equal to $L$,then the value of $(6L + 1)$ is

The value of $\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is

The solution of the equation $\sin ^{-1} x+\sin ^{-1} 2 x=\frac{\pi}{3}$ is