Explanation

(b)
$\tan{(70{^\circ} - 20{^\circ}) = \frac{\tan{70{^\circ} - \tan{20{^\circ}}}}{1 + \tan{70{^\circ}\tan{20{^\circ}}}}}$
$\Rightarrow \ \tan{50{^\circ}\left( 1 + \tan{70{^\circ}\tan{20{^\circ}}} \right) = \tan{70{^\circ} - \tan{20{^\circ}}}}$ …(i)
Now, $\tan{(70{^\circ} + 20{^\circ})} = \frac{\tan{70{^\circ} + \tan{20{^\circ}}}}{1 - \tan{20{^\circ}\tan{70{^\circ}}}}$
$\Rightarrow \ \tan{20{^\circ}\tan{70{^\circ} = 1}\ \ \ \ \ \ \ \lbrack{\because tan}{90{^\circ} = \infty}\rbrack}$
On putting in Eq. (i), we get
$\tan{50{^\circ}(1 + 1) = \tan{70{^\circ} - \tan{20{^\circ}}}}$
$\Rightarrow \ \tan{20{^\circ} + 2\tan{50{^\circ} - \tan{70{^\circ} = 0}}}$