Question

\(\frac{2tan 30 ^\circ}{1-tan^2 30 ^\circ}=\)

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\frac{2\tan {30}^{\circ }}{1-{\tan }^2{30}^{\circ }}=\frac{2\times \frac{1}{\sqrt{3}}}{1-(\frac{1}{\sqrt{3}}{)}^2}=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}=\frac{\frac{2}{\sqrt{3}}}{\frac{2}{3}}=\sqrt{3}=\tan {60}^{\circ }$