I want to explain the latest steps from this Q

What does $50 - 20$ equal?

Edit: Your actual working out seems a bit backward.

You are trying to use the identity

$\tan{(\alpha - \beta)} = \frac{\tan{\alpha} - \tan{\beta}}{1 + \tan{\alpha}\tan{\beta}}$

to simplify

$\frac{\tan{50^\circ} - \tan{20^\circ}}{1 + \tan{50^\circ}\tan{20^\circ}}$ .

$\frac{\tan{50^\circ} - \tan{20^\circ}}{1 + \tan{50^\circ}\tan{20^\circ}} = \tan{(50^\circ - 20^\circ)}$

$= \tan{30^\circ}$

$= \frac{1}{\sqrt{3}}$

$= \frac{\sqrt{3}}{3}$ .