Explanation

(d)
$\cos^{- 1}{x,\sin^{- 1}x}\$are real, if $- 1 \leq x \leq 1$
But $\cos^{- 1}{x > \sin^{- 1}x}$
$\Rightarrow 2\cos^{- 1}{x > \frac{\pi}{2}}$
$\Rightarrow \cos^{- 1}x = \frac{\pi}{4}$
$\therefore$ cos ($\cos^{- 1}{x) < \cos\frac{\pi}{4}}$
$\Rightarrow x < \frac{1}{\sqrt{2}}$
The common value are $- 1 \leq x < \frac{1}{\sqrt{2}}$