Question

If $x=\frac{2\tan {30}^{\circ }}{1-{\tan }^2{30}^{\circ }}$, then the value of $x$ is:

• A. $\tan {45}^{\circ }$
• B. $\tan {30}^{\circ }$
• C. $\tan {60}^{\circ }$
• D. $\tan {90}^{\circ }$

Answer 1

The correct option is C $\tan {60}^{\circ }$

$x=\frac{2\tan 30°}{1-{\tan }^{2}30°}=\frac{2\times \frac{1}{\sqrt{3}}}{1-{\left(\frac{1}{\sqrt{3}}\right)}^2}=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}$

$\Rightarrow x=\frac{2}{\sqrt{3}}\times \frac{3}{2}=\sqrt{3}=\tan 60°$

$\Rightarrow x=\tan 60°.$

Hence, the answer is $\tan 60°.$