Explanation

(c)
Given that , $\cos^{- 1}{x + \cos^{- 1}{y + \cos^{- 1}{\mathcal{z} = 3\pi}}}$
$\because 0 \leq \cos^{- 1}{x \leq \pi}$
Similarly, $0 \leq \cos^{- 1}{y \leq \pi}$
And $0 \leq \cos^{- 1}{\mathcal{z \leq}\pi}$
Here, $\cos^{- 1}{xcos^{- 1}y = \cos^{- 1}{\mathcal{z =}\pi}}$
$\Rightarrow x = y = \mathcal{z =}\cos{\pi = - 1}$
$\therefore xy + y\mathcal{z + z}x = ( - 1)( - 1) + ( - 1)( - 1) + ( - 1)( - 1)$
=1+1+1=3