$\sin^{-1} x + \cos^{-1} x$ is equal to

Consider the following statements:
Assertion $(A)$: When $x, y, z$ are positive numbers, then $\operatorname{Tan}^{-1}\left(\sqrt{\frac{x(x+y+z)}{y z}}\right)+\operatorname{Tan}^{-1}\left(\sqrt{\frac{y(x+y+z)}{x z}}\right)+\operatorname{Tan}^{-1}\left(\sqrt{\frac{z(x+y+z)}{x y}}\right) = \pi$
Reason $(R)$: $\operatorname{Tan}^{-1} a + \operatorname{Tan}^{-1} b = \operatorname{Tan}^{-1}\left(\frac{a+b}{1-ab}\right)$ if $a > 0$ and $b > 0$ and $ab < 1$.

Find the sum of the series: $\tan^{-1} \left( \frac{1}{1 + 1 \times 2} \right) + \tan^{-1} \left( \frac{1}{1 + 2 \times 3} \right) + \dots + \tan^{-1} \left( \frac{1}{1 + n(n + 1)} \right) =$

Evaluate: ${\cot ^{ - 1}}3 + {\csc ^{ - 1}}\sqrt 5 = $

If $\sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \frac{\pi}{2}$,then the value of $x^2 + y^2 + z^2 + 2xyz$ is equal to

The solution of $\tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}$ is