Question

Choose the correct option and justify your choice :
$\frac{2\tan {30}^{\circ }}{1-{\tan }^2{30}^{\circ }}=$

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $2$
• D. $\sqrt{2}$

Answer 1

Answer: (A)

$\sqrt{3}$

We know that $\tan {30}^0=\frac{1}{\sqrt{3}}$

The value of $\frac{2\tan {30}^o}{1-{\tan }^2{30}^o}$

$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-{\left(\frac{1}{\sqrt{3}}\right)}^2}=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}=\frac{\frac{2}{\sqrt{3}}}{\frac{2}{3}}=\sqrt{3}$