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Let A and B be positive acute angles such that 3cos² A + 2cos² B = 4 and (3sin A)/(sin B) = (2cos B)/(cos A). Then the value of A + 2B is

1. π/6
2. π/2
3. π/3
4. π/4

Correct answer: π/2

Solution

The equations given can be manipulated to find the relationships between angles A and B. By solving these equations, we find that A and B satisfy specific trigonometric identities that lead to the conclusion that A + 2B equals π/2.

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