Explanation

(b)
$\frac{\cos{70{^\circ}}}{\sin{70{^\circ}}} + 4\cos{70{^\circ} = \frac{\cos{70{^\circ} + 4\sin{70{^\circ}\cos{70{^\circ}}}}}{\sin{70{^\circ}}}}$
$= \frac{\cos{70{^\circ} + 2\sin{140{^\circ}}}}{\sin{70{^\circ}}}$
$= \frac{\sin{20{^\circ} + 2\sin{40{^\circ}}}}{\sin{70{^\circ}}}$
$= \frac{2\sin{30{^\circ}\cos{10{^\circ} + \sin{40{^\circ}}}}}{\sin{70{^\circ}}}$
$\frac{\sin{80{^\circ} + \sin{40{^\circ}}}}{\sin{70{^\circ}}}$
$= \frac{2\sin{60{^\circ}\cos{20{^\circ}}}}{\sin{70{^\circ}}}$
$= \frac{2\left( \frac{\sqrt{3}}{2} \right)\sin{70{^\circ}}}{\sin{70{^\circ}}} = \sqrt{3}$