Question

The value of
$\frac{2tan{30}^{\circ }}{1-ta{n}^2{30}^{\circ }}$ is _______.

• A. $tan{30}^{\circ }$
• B. $tan{60}^{\circ }$
• C. $tan{0}^{\circ }$
• D. $tan{90}^{\circ }$

Answer 1

The correct option is B

$tan{60}^{\circ }$

$\frac{2tan{30}^{\circ }}{1-ta{n}^2{30}^{\circ }}$

$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-{\left(\frac{1}{\sqrt{3}}\right)}^2}$ $(\because tan{30}^{\circ }=\frac{1}{\sqrt{3}})$

$=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}$

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

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

$=\sqrt{3}$

$=tan{60}^{\circ }$