2021 · Q46
If sec θ + cos θ = 5/2, where 0 ≤ θ ≤ 90°, then what is the value of sin²θ?
Elementary MathematicsTrigonometry
- A1/4
- B1/2
- C3/4
- D1
Explanation
Multiply secθ + cosθ = 5/2 by cosθ: 1 + cos²θ = (5/2)cosθ, i.e. 2cos²θ − 5cosθ + 2 = 0. Factoring, (2cosθ − 1)(cosθ − 2) = 0; cosθ = 2 is impossible, so cosθ = 1/2. Then sin²θ = 1 − 1/4 = 3/4. Hence option C.