Question

Verify:

$\frac{2\tan {30}^o}{1-{\tan }^2{30}^o}=\sqrt{3}$

Answer 1

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

$=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}$ [Since $\tan {30}^o=\frac{1}{\sqrt{3}}$]

$=\frac{2\sqrt{3}}{2}$

$=\sqrt{3}$