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    Question

    If sin α + cos β = 2 (0˚ ≤ β < α ≤ 90˚), then

    sin[(2α + β)/3] =?
    A √2/3 Correct Answer Incorrect Answer
    B √3/4 Correct Answer Incorrect Answer
    C √3/2 Correct Answer Incorrect Answer
    D √3 Correct Answer Incorrect Answer

    Solution

    sin α + cos β = 2 sin α ≤ 1; cos β ≤ 1 => α = 90˚ ; β = 0˚    sin[(2α + β)/3] = sin (180˚/3) = sin 60˚ = √3/2

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