Explanation

(d)
Given, $\cos^{- 1}{x + \cos^{- 1}{y + \cos^{- 1}{z = 3\pi}}}$
And we know that $0 \leq \cos^{- 1}{x \leq \pi}$
$\therefore$ We know
$\cos^{- 1}{x = \pi,\cos^{- 1}{y = \pi,\ \cos^{- 1}{z = \pi}}}$
$\therefore\ \ x = y = z = \cos{\pi = - 1}$
$\therefore xy + yz + zx = ( - 1)( - 1) + ( - 1)( - 1) + ( - 1)( - 1) = 3$