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°

Choose the correct option and justify your choice :

$\dfrac{\text{1 - tan}^2 45°}{\text{1 + tan}^2 45°} =$

1. tan 90°

2. 1

3. sin 45°

4. 0

Choose the correct option and justify your choice :

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

1. cos 60°

2. sin 60°

3. tan 60°

4. sin 30°

If tan (A + B) = $\sqrt{3}$ and tan (A – B) = $\dfrac{1}{\sqrt{3}}$; 0° < A + B ≤ 90°; A > B, find A and B.