Question

$\frac{2\tan {30}^{\circ }}{1+{\tan }^2{30}^{\circ }}=$

• A. $\sin {60}^{\circ }$
• B. $\cos {60}^{\circ }$
• C. $\tan {60}^{\circ }$
• D. $\sin {30}^{\circ }$

Answer 1

The correct option is A $\sin {60}^{\circ }$

$\frac{2\tan {30}^{\circ }}{1+{\tan }^2{30}^{\circ }}=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1+(\frac{1}{\sqrt{3}}{)}^2}$
$=\frac{\left(\frac{2}{\sqrt{3}}\right)}{(1+\frac{1}{3})}=\frac{\frac{2}{\sqrt{3}}}{\frac{4}{3}}$
$=\frac{\sqrt{3}}{2}=\sin {60}^{\circ }$