Evaluate: $\sec^{-1} x + \operatorname{cosec}^{-1} x + \cos^{-1}(x^{-1}) + \sin^{-1}(x^{-1})$ (where $|x| > 1, x \in R$)

$\frac{1}{2}{\cos ^{ - 1}}\left( {\frac{{1 - x}}{{1 + x}}} \right) = $

The set of all values of $k$ for which $(\tan^{-1} x)^3 + (\cot^{-1} x)^3 = k \pi^3$,$x \in \mathbb{R}$,is the interval

If $\alpha$ and $\beta$ are angles in the first quadrant such that $\tan \alpha = \frac{1}{7}$ and $\sin \beta = \frac{1}{\sqrt{10}}$,then $\alpha + 2\beta =$ (in $^{\circ}$)

If $\cos ^{-1}\left(\frac{12}{13}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1} P$,then the value of $P$ is

$\sin ^{-1}\left(\cos \frac{\pi}{13}\right)+\cos ^{-1}\left(\sin \frac{\pi}{13}\right) = $ . . . . . . .