2022 · Q50
If y = cos² x + sec² x, where 0 ≤ x < (π)/(2), then which one of the following is correct?
Elementary MathematicsTrigonometry
- A0
- B0.5 ≤ y
- C1 ≤ y
- Dy ≥ 2
Explanation
Put t = cos^2(x); on [0, pi/2) we have 0 < t <= 1 and y = t + 1/t. By AM >= GM, t + 1/t >= 2 with equality at t = 1, so y >= 2 always. Option (d) is therefore the sharpest correct description of the range. (Option (c), 1 <= y, is implied by it but weaker, so (d) is the intended best answer.)