If A = 30° ; 3 sin A - 4 sin³ A is equal to:

1. cos 3A

2. tan 3A

3. sin 3A

4. cot 3A

3 sin A - 4 sin³ A = 3 sin 30° - 4 sin³ 30°

$= 3 \times \dfrac{1}{2} - 4 \times \Big(\dfrac{1}{2}\Big)^2\\[1em] = \dfrac{3}{2} - 4 \times \dfrac{1}{8}\\[1em] = \dfrac{3}{2} - \dfrac{1}{2}\\[1em] = \dfrac{3 - 1}{2} \\[1em] = \dfrac{2}{2} \\[1em] = 1\\[1em] = \text{sin 90°}\\[1em] = \text{sin 3 x 30°}\\[1em] = \text{sin 3A}\\[1em]$

Hence, option 3 is the correct option.