If A = 30°, then cos⁴ A - sin⁴ A is equal to :

1. sin 60°

2. tan 60°

3. cot 60°

4. cos 60°

cos⁴ A - sin⁴ A = cos⁴ 30° - sin⁴ 30°

$= \Big(\dfrac{\sqrt3}{2}\Big)^4 - \Big(\dfrac{1}{2}\Big)^4\\[1em] = \dfrac{9}{16} - \dfrac{1}{16}\\[1em] = \dfrac{9 - 1}{16}\\[1em] = \dfrac{8}{16}\\[1em] = \dfrac{1}{2}\\[1em] = \text {cos 60°}$

Hence, option 4 is the correct option.