2021 · Q59
What is the ratio of the greatest to the smallest value of 2 − 2 sin x − sin²x, 0 ≤ x ≤ (π/2)?
Elementary MathematicsTrigonometry
- A−2
- B−1
- C1
- D2
Explanation
With t = sinx ∈ [0, 1], the expression is 2 − 2t − t² = 3 − (t+1)², decreasing in t. Greatest value 2 (at t = 0), smallest −1 (at t = 1). Their ratio is 2/(−1) = −2. Hence option A.