$\dfrac{\text{tan 60° - tan 30°}}{1 + \text{tan 60° tan 30°}}$ is equal to :

1. tan 30°

2. tan 45°

3. tan 60°

4. none

Solving,

$\Rightarrow \dfrac{\text{tan 60° - tan 30°}}{1 + \text{tan 60° tan 30°}} \\[1em] \Rightarrow \dfrac{\sqrt{3} - \dfrac{1}{\sqrt{3}}}{1 + \sqrt{3} \times \dfrac{1}{\sqrt{3}}} \\[1em] \Rightarrow \dfrac{\dfrac{3 - 1}{\sqrt{3}}}{1 + 1} \\[1em] \Rightarrow \dfrac{\dfrac{2}{\sqrt{3}}}{2} \\[1em] \Rightarrow \dfrac{2}{2\sqrt{3}} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} \\[1em] \Rightarrow \text{tan 30°}.$

Hence, Option 1 is the correct option.