If A and B are acute angles such that \( 2A + 2B = \pi \), then what is the maximum value of \( \sin A \cdot \sin B \) ?
- A. \frac{1}{2} ✓
- B. \frac{1}{4}
- C. \frac{\sqrt{3}}{4}
- D. 1
Correct Answer: A. \frac{1}{2}
Explanation
Since \( 2A + 2B = \pi \), \( B = \frac{\pi}{2} - A \), making \( \sin B = \cos A \). The product becomes \( \sin A \cos A = \frac{1}{2}\sin 2A \), which has a maximum value of \( \frac{1}{2} \).
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