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

Correct option is A

Given: ​$$\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$$

Solution:

We know that,

​$$\tan 30^\circ = \frac{1}{\sqrt{3}}$$

Now, substitute this value into the expression, $$\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$$​​

= $$\frac{\frac{2 }{\sqrt{3}}}{1 + \frac{1}{3}}$$​

= $$\frac{(\frac{2}{ \sqrt{3}})}{(\frac{4}{3})}$$​​
= $$\left( \frac{2}{\sqrt{3}} \right) \times \left( \frac{3}{4} \right)$$​​
=  $$\frac{\sqrt{3}}{2}$$​​

= $$\sin 60^\circ$$

Thus, the correct answer is (a).