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Determine the maximum value attained by the function f(x) = sin 2x / sin(x + π/4) for x in the interval [0, π/2].

1. 1
2. 2
3. 3
4. None of these

Correct answer: 1

Solution

The maximum value of the function occurs when the numerator, sin 2x, reaches its peak of 1, while the denominator, sin(x + π/4), remains positive and does not exceed 1 in the given interval, ensuring that the overall value does not exceed 1.

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