Choose the correct option and justify your choice :

$\dfrac{\text{2 tan 30°}}{\text{1 + tan}^2 30°} =$

1. sin 60°

2. cos 60°

3. tan 60°

4. sin 30°

Solving,

$\Rightarrow \dfrac{\text{2 tan 30°}}{\text{1 + tan}^2 30°} = \dfrac{2 \times \dfrac{1}{\sqrt{3}}}{1 + \Big(\dfrac{1}{\sqrt{3}}\Big)^2} \\[1em] = \dfrac{\dfrac{2}{\sqrt{3}}}{1 + \dfrac{1}{3}} \\[1em] = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{3 + 1}{3}} \\[1em] = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{4}{3}} \\[1em] = \dfrac{2 \times 3}{4 \times \sqrt{3}} \\[1em] = \dfrac{\sqrt{3}}{2} \\[1em] = \text{sin 60°}.$

Hence, Option 1 is the correct option.