Evaluate the following :

$\dfrac{5\text{ cos}^2 60° + 4\text{ sec}^2 30° - \text{ tan}^2 45°}{\text{sin}^2 30° + \text{ cos}^2 30°}$

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 :

sin 2A = 2 sin A is true when A =

1. 0°

2. 30°

3. 45°

4. 60°

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°