2023 · Q53
If 2 cos² θ + sin θ - 2 = 0, 0 < θ ≤ (π)/(2), then what is the value of θ?
Elementary MathematicsTrigonometry
- Aπ/6
- Bπ/4
- Cπ/3
- Dπ/2
Explanation
Replacing cos²θ by 1 − sin²θ gives 2(1 − sin²θ) + sinθ − 2 = 0, i.e. sinθ(1 − 2sinθ) = 0. With 0 < θ ≤ π/2, sinθ = 1/2 (sinθ = 0 is excluded), so θ = π/6 (A).