Hi
I want to explain the latest steps from this Q
What does $\displaystyle 50 - 20$ equal?
Edit: Your actual working out seems a bit backward.
You are trying to use the identity
$\displaystyle \tan{(\alpha - \beta)} = \frac{\tan{\alpha} - \tan{\beta}}{1 + \tan{\alpha}\tan{\beta}}$
to simplify
$\displaystyle \frac{\tan{50^\circ} - \tan{20^\circ}}{1 + \tan{50^\circ}\tan{20^\circ}}$.
$\displaystyle \frac{\tan{50^\circ} - \tan{20^\circ}}{1 + \tan{50^\circ}\tan{20^\circ}} = \tan{(50^\circ - 20^\circ)}$
$\displaystyle = \tan{30^\circ}$
$\displaystyle = \frac{1}{\sqrt{3}}$
$\displaystyle = \frac{\sqrt{3}}{3}$.