Explanation

(a)
Given equation is
$2\cos^{- 1}{x + \sin^{- 1}{x = \frac{11\pi}{6}}}$
$\Rightarrow \cos^{- 1}{x + (\cos^{- 1}{x + \sin^{- 1}{x) = \frac{11\pi}{6}}}}$
$\Rightarrow \cos^{- 1}{x + \frac{\pi}{2} = \frac{11\pi}{6}}$
$\Rightarrow \cos^{- 1}{x = \frac{4\pi}{3}}$
Which is not possible as $\cos^{- 1}{x \in \lbrack 0,\ \pi\rbrack.}$