Question

$\frac{\tan 60°-\tan 30°}{1+\tan 60°.\tan 30°}=$

• A. $\sqrt{3}$
• B. $3$
• C. $\frac{1}{\sqrt{3}}$
• D. $1$

Answer 1

The correct option is C

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

Explanation for the correct option:

Evaluating the expression:

$\frac{\tan 60°-\tan 30°}{1+\tan 60°.\tan 30°}$

Putting up the values, we have:

$$\begin{gathered} =\frac{\sqrt{3}-{\displaystyle \frac{1}{\sqrt{3}}}}{1+\sqrt{3}\times {\displaystyle \frac{1}{\sqrt{3}}}}\left[\tan 60°=\sqrt{3},\tan 30°=\frac{1}{\sqrt{3}}\right] \\ =\frac{{\displaystyle \frac{3-1}{\sqrt{3}}}}{1+{\displaystyle \frac{\sqrt{3}}{\sqrt{3}}}}=\frac{{\displaystyle \frac{2}{\sqrt{3}}}}{2} \\ =\frac{2}{\sqrt{3}}\times \frac{1}{2}=\frac{1}{\sqrt{3}} \end{gathered}$$

Hence, option (C) is the correct answer