Evaluate: $\cot ^{ - 1}\left(\frac{xy + 1}{x - y}\right) + \cot ^{ - 1}\left(\frac{yz + 1}{y - z}\right) + \cot ^{ - 1}\left(\frac{zx + 1}{z - x}\right)$

$2 \tan^{-1}(\cos x) = \tan^{-1}(\csc^2 x)$,then $x = $

If $\pi \leq x \leq 2 \pi$,then $\cos^{-1}(\cos x)$ is equal to :-

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

If $\tan^{-1} \left[ \frac{\sqrt{5} - 2\sqrt{6}}{1 + \sqrt{6}} \right] = \frac{\pi}{3} - \tan^{-1}(k)$, then $\sec^{-1}(k) = \dots$

If ${x_1}, {x_2}, {x_3}, {x_4}$ are roots of the equation ${x^4} - {x^3}\sin 2\beta + {x^2}\cos 2\beta - x\cos \beta - \sin \beta = 0$,then ${\tan ^{ - 1}}{x_1} + {\tan ^{ - 1}}{x_2} + {\tan ^{ - 1}}{x_3} + {\tan ^{ - 1}}{x_4} = $