Question

\[\frac{\tan 60^\circ - \tan 30^\circ}{1 + \tan 60^\circ \tan 30^\circ}\] is equal to ______.

Options

• tan 30°

• tan 45°

• tan 60°

• none

Answer 1

\[\frac{\tan 60^\circ - \tan 30^\circ}{1 + \tan 60^\circ \tan 30^\circ}\] is equal to \[\underline{\boldsymbol{tan 30°}}\]. 

Explanation:

Solving,

\[\Rightarrow \frac{\tan 60^\circ - \tan 30^\circ}{1 + \tan 60^\circ \tan 30^\circ}\]

\[\Rightarrow \frac{\sqrt{3} - \frac{1}{\sqrt{3}}}{1 + \sqrt{3} \times \frac{1}{\sqrt{3}}}\]

\[\Rightarrow \frac{\frac{3 - 1}{\sqrt{3}}}{1 + 1}\]

\[\Rightarrow \frac{\frac{2}{\sqrt{3}}}{2}\]

\[\Rightarrow \frac{2}{2\sqrt{3}}\]

\[\Rightarrow \frac{1}{\sqrt{3}}\]

\[\Rightarrow \tan 30^\circ\]