Explanation

(b)
Since, $1\ radian = \frac{7\pi}{22}$
$\therefore\ \ 12\ radian = \frac{7\pi}{22} \times 12 = \frac{42\pi}{11} = 4\pi - \frac{2\pi}{11}$
And $14\ radian = \frac{7\pi}{22} \times 14 = \frac{49\pi}{11}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 4\pi + \frac{5\pi}{11}$
$\therefore\ \cos^{- 1}{(\cos{12)} - \sin^{- 1}{(\sin 14)}}$
$\ \ \ \ \ \ \ \ = \cos^{- 1}{\cos\left( 4\pi - \frac{2\pi}{11} \right)} - \sin^{- 1}\left\lbrack \sin\left( 4\pi + \frac{5\pi}{11} \right) \right\rbrack$
$\ \ \ \ \ \ \ = \cos^{- 1}{\cos\left( \frac{2\pi}{11} \right)} - \sin^{- 1}\left( \sin\frac{5\pi}{11} \right)$
$\ \ \ \ \ \ \ = 4\pi - 12 - (14 - 4\pi) = 8\pi - 26$