The value of :

cos² 60° - 2 sin³ 30° + 3 cot⁴ 45° is :

1. 1

2. -2

3. 3

4. 2

$\text{cos}^2 60° - 2 \text{sin}^3 30° + 3 \text{cot}^4 45° = \Big(\dfrac{1}{2}\Big)^2 - 2 \times \Big(\dfrac{1}{2}\Big)^3 + 3 \times (1)^2\\[1em] = \dfrac{1}{4} - 2 \times \dfrac{1}{8} + 3\\[1em] = \dfrac{1}{4} - \dfrac{1}{4} + 3\\[1em] = 3$

Hence, option 3 is the correct option.