2024 · Q34
What is the minimum value of (sin²A+5sinA+1)/(sinA) for 0 < A ≤ (π )/(2) ?
Elementary MathematicsTrigonometry
- A3
- B5
- C7
- D9
Explanation
(sin²A + 5sinA + 1)/sinA = sinA + 5 + cosecA, which decreases as sinA increases on (0, 1]. Its minimum is therefore at sinA = 1 (A = 90°). The minimum value is 1 + 5 + 1 = 7, option (c).