Explanation

(c)
$\cos{(4095{^\circ}) = \cos{(45 \times 90{^\circ} + 45{^\circ})}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - \sin{45{^\circ}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - \sin\frac{\pi}{4}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sin\left( - \frac{\pi}{4} \right)$
$\therefore\ \ \sin^{- 1}{\{\cos{(4095{^\circ})}\}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sin^{- 1}{\sin\left( - \frac{\pi}{4} \right)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - \frac{\pi}{4}$