Explanation

(c)
$\frac{\cos{12{^\circ} - \sin{12{^\circ}}}}{\cos{12{^\circ} + \sin{12{^\circ}}}} + \frac{\sin{147{^\circ}}}{\cos{147{^\circ}}}$
$= \frac{1 - \tan{12{^\circ}}}{1 + \tan{12{^\circ}}} + \tan{147{^\circ}}$
$= \tan{(45{^\circ} - 12{^\circ}) + \tan{(180{^\circ} - 33{^\circ})}}$
$= \tan{33{^\circ} - \tan{33{^\circ} = 0}}$