Question 2
TrigonometryIf 2cos2θ = 1 + sin θ, 0° ≤ θ ≤ 90°, find the value of θ.
- A.30°
- B.45°
- C.60°
- D.90°
Show the answer and explanation
Answer: A (30°)
Explanation
Replace cos²θ by 1 − sin²θ: 2 − 2sin²θ = 1 + sin θ, so 2sin²θ + sin θ − 1 = 0, i.e. (2sin θ − 1)(sin θ + 1) = 0. In the range, sin θ = ½, so θ = 30°.