Explanation

(b)
Given, $\sin^{- 1}{x - \cos^{- 1}{x = \cos^{- 1}\left( \frac{\sqrt{3}}{2} \right)}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \sin^{- 1}{x - \cos^{- 1}{x = \frac{\pi}{6}}}$ …(i)
But $\sin^{- 1}{x + \cos^{- 1}{x = \frac{\pi}{2}}}$ …(ii)
On solving Eqs. (i) and (ii), we get
$\sin^{- 1}{x = \frac{\pi}{3}}$ and $\cos^{- 1}{x = \frac{\pi}{6}}$
$\Rightarrow \ \ \ x = \frac{\sqrt{3}}{2}$ is the unique solution.