\( \cos x + \sqrt{3} \sin x \) is maximum when x is equal to
- A. \frac{\pi}{2}
- B. \frac{\pi}{3} ✓
- C. \frac{\pi}{4}
- D. \frac{\pi}{6}
Correct Answer: B. \frac{\pi}{3}
Explanation
The expression can be rewritten as 2(\frac{1}{2}\cos x + \frac{\sqrt{3}}{2}\sin x) = 2\sin(x + \frac{\pi}{6}). The sine function is maximum at \pi/2, so x + \pi/6 = \pi/2, meaning x = \pi/3.
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