Explanation

(b)
$\cos^{- 1}{p + \cos^{- 1}{q + \cos^{- 1}{r = 3\pi}}}$
We know that, if $y = \cos^{- 1}x,$ then $- 1 \leq x \leq 1$ and $0 \leq y \leq \pi$,
Hence, the given equation will hold only when each is $\pi$
$\therefore\ \ p = q = r = \cos{\pi = - 1}$
$\therefore p^{2} + q^{2} + r^{2} + 2pqr$
$\ \ \ \ \ \ = ( - 1)^{2} + ( - 1)^{2} + ( - 1)^{2} + 2( - 1)( - 1)( - 1)$
$\ \ \ \ \ \ = 1 + 1 + 1 - 2$
$\ \ \ \ \ \ = 3 - 2 = 1$