Explanation

(b)
Given that, $x^{2} + y^{2} + \mathcal{z}^{2} = r^{2}$
Now, $\tan^{- 1}{\left( \frac{xy}{\mathcal{z}r} \right) + \tan^{- 1}{\left( \frac{y\mathcal{z}}{xe} \right) + \tan^{- 1}\left( \frac{x\mathcal{z}}{yr} \right)}}$
$= \tan^{- 1}\left\lbrack \frac{\frac{xy}{\mathcal{z}r} + \frac{y\mathcal{z}}{xr} + \frac{x\mathcal{z}}{yr} - \frac{xy\mathcal{z}}{r^{3}}}{1 - \left( \frac{x^{2} + y^{2} + \mathcal{z}^{2}}{r^{2}} \right)} \right\rbrack$
$= \tan^{- 1}\left\lbrack \frac{\frac{xy}{\mathcal{z}r} + \frac{y\mathcal{z}}{xr} + \frac{x\mathcal{z}}{yr} - \frac{xy\mathcal{z}}{r^{3}}}{1 - \frac{r^{2}}{r^{2}}} \right\rbrack$
$= \tan^{- 2}{\infty = \frac{\pi}{2}}$