2022 · Q48
What is the minimum value of sin⁴ θ + cos⁴ θ - 2sin² θ cos²θ?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- DMinimum value does not exist
Explanation
sin⁴θ+cos⁴θ-2sin²θcos²θ = (sin²θ-cos²θ)² = cos²2θ ≥ 0, attaining 0 at θ = 45°. Hence the keyed option is A.