2021 · Q52
If (cos²θ − 3cosθ + 2)/sinθ = 1 where 0° < θ < 90°, then what is sin²θ + cosθ equal to ?
Elementary MathematicsTrigonometry
- A5/4
- B3/2
- C7/4
- D2
Explanation
The equation gives cos²θ − 3cosθ + 2 = sinθ > 0. Solving numerically in (0°, 90°) yields cosθ ≈ 0.4253, sinθ ≈ 0.9051 (check: LHS ≈ 0.9051). Then sin²θ + cosθ ≈ 0.8193 + 0.4253 = 1.2444 ≈ 5/4. This is option (a).