Explanation

(a)
$\tan{(70{^\circ})} = \tan{(50{^\circ} + 20{^\circ})} = \frac{\tan{50{^\circ} + \tan{20{^\circ}}}}{1 - \tan{50{^\circ}\tan{20{^\circ}}}}$
$\Rightarrow \ \tan{70{^\circ} - \left( \tan{50{^\circ}\tan{20{^\circ}}} \right)\tan{70{^\circ} = \tan{50{^\circ} + \tan{20{^\circ}}}}}$
$\Rightarrow \ \tan{70{^\circ} - \cot{20{^\circ}\tan{20{^\circ}\tan{50{^\circ} = \tan{50{^\circ} + \tan{20{^\circ}}}}}}}$
[using, $\tan{(90{^\circ} - \theta = \cot\theta)}$]
$\Rightarrow \ \tan{70{^\circ} - \tan{50{^\circ} = \tan{50{^\circ} + \tan{20{^\circ}}}}}$
$\Rightarrow \ \tan{70{^\circ} - \tan{20{^\circ} = 2\tan{50{^\circ}}}}$
$\Rightarrow \ \frac{\tan{70{^\circ} - \tan{20{^\circ}}}}{\tan{50{^\circ}}} = 2$