The value of $\cos \left[\sec ^{-1} x+\operatorname{cosec}^{-1} x\right], |x| \geq 1$ is equal to: . . . . . . .

If $2 \sinh^{-1}\left(\frac{a}{\sqrt{1-a^2}}\right)=\log \left(\frac{1+x}{1-x}\right)$, then $x$ is equal to

The value of $\cot ^{-1}(-\sqrt{3})-\tan ^{-1} \sqrt{3}$ is equal to . . . . . . .

If $\alpha$ and $\beta$ are the least and the greatest values of $f(x)=(\sin ^{-1} x)^2+(\cos ^{-1} x)^2$ for all $x \in [-1, 1]$ respectively,then $8(\alpha+\beta)=$

For $\theta \in \left(0, \frac{\pi}{2}\right)$, $\operatorname{sech}^{-1}(\cos \theta)$ is equal to

$(\tan ^{-1} x)^2+(\cot ^{-1} x)^2=\frac{5 \pi^2}{8} \Rightarrow x=$