2025 · Q28
If cot²θ - 3√3 cotθ + 6 = 0, where (π)/(6) < θ < (π)/(2), then what is the value of sinθ + cos 2θ?
Elementary MathematicsTrigonometry
- A0
- B1
- C3
- D1+2
Explanation
The quadratic in cotθ has discriminant (3√3)² − 24 = 3, giving cotθ = (3√3 ± √3)/2, i.e. 2√3 or √3. On (π/6, π/2) the admissible root is cotθ = √3, so θ = π/6. Then sinθ + cos 2θ = sin 30° + cos 60° = 1/2 + 1/2 = 1, option (b).