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For which value of x in the interval (0, π/2) does the expression sin(x + π/6) + cos(x + π/6) attain its greatest value?

1. π/6
2. π/12
3. π/3
4. π/4

Correct answer: π/12

Solution

The expression sin(x + π/6) + cos(x + π/6) can be maximized by recognizing that it is equivalent to the sine of a shifted angle. The maximum occurs when the angle x + π/6 is equal to π/4, which corresponds to x = π/12, thus yielding the highest value in the given interval.

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