If y=\cos^2x+\sec^2x, where 0 \leq x \lt \frac{\pi}{2}, then which one of the following is correct?
- A. 0 \lt y \lt 0.5
- B. 0.5 \leq y \lt 1
- C. 1 \leq y \lt 2
- D. y \geq 2 ✓
Correct Answer: D. y \geq 2
Explanation
Using the AM-GM inequality, the sum of a positive number and its reciprocal is always at least 2. Alternatively, y = (\cos x - \sec x)^2 + 2 \geq 2. Therefore, y \geq 2.
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