Question

Solve:
$\frac{2\tan 30}{1+{\tan }^{2}30}$

Answer 1

As we know that,

$\sin 2\theta =\frac{2\tan \theta }{1+{\tan }^2\theta }$

Therefore, for $\theta =30°$

$\sin (2\times 30°)=\frac{2\tan 30°}{1+{\tan }^{2}30°}$

$\Rightarrow \frac{2\tan 30°}{1+{\tan }^{2}30°}=\sin 60°=\frac{\sqrt{3}}{2}$