Explanation

(c)
$\sqrt{3}cosec\ 20{^\circ} - \sec{20{^\circ}}$
$= \frac{\tan{60{^\circ}}}{\sin{20{^\circ}}} - \frac{1}{\cos{20{^\circ}}}$
$= \frac{\sin{60{^\circ}\cos{20{^\circ} - \sin{20{^\circ}\cos{60{^\circ}}}}}}{\cos 60{^\circ}\sin{20{^\circ}\cos{20{^\circ}}}}$
$= \frac{2\sin{20{^\circ}\cos{20{^\circ}}}}{\frac{1}{2}(\sin{20{^\circ}\cos{20{^\circ}}})} = 4$