Explanation

(c)
$\alpha + \beta = \sin^{- 1}{\frac{\sqrt{3}}{2} + \cos^{- 1}{\frac{\sqrt{3}}{2} + \sin^{- 1}{\frac{1}{3} + \cos^{- 1}\frac{1}{3}}}}$
$= \frac{\pi}{2} + \frac{\pi}{2} = \pi$
Also, $\alpha = \frac{\pi}{3} + \sin^{- 1}\frac{1}{3} < \frac{\pi}{3} + \sin^{- 1}\frac{1}{2}$
As $\sin\theta$ is increasing in $\left\lbrack 0,\ \frac{\pi}{2} \right\rbrack$
$\therefore\ \ \alpha < \frac{\pi}{3} + \frac{\pi}{6} = \frac{\pi}{2}$
$\Rightarrow \ \beta > \frac{\pi}{2} > \alpha$
$\Rightarrow \ \ \alpha < \beta$