If sin α = $\dfrac{1}{2},$ then the value of 3 cos α - 4 cos³ α is

1. -1

2. 0

3. 1

4. 2

Given,

⇒ sin α = $\dfrac{1}{2}$

⇒ sin α = sin 30°

⇒ α = 30°.

$\text{3 cos α - 4 cos}^3 α = 3\text{ cos 30° - 4 cos}^3 30° \\[1em] = 3 \times \dfrac{\sqrt{3}}{2} - 4 \times \Big(\dfrac{\sqrt{3}}{2}\Big)^3 \\[1em] = \dfrac{3\sqrt{3}}{2} - 4 \times \dfrac{3\sqrt{3}}{8} \\[1em] = \dfrac{3\sqrt{3}}{2} - \dfrac{3\sqrt{3}}{2} \\[1em] = 0.$

Hence, Option 2 is the correct option.