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    Question

    If sin(A + B) = √3/2 and cos(A + 2B) = 1/2, where 0°

    A, B < 90°, then find the value of tan(2A).
    A √3 Correct Answer Incorrect Answer
    B -√3 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer

    Solution

    sin(A + B) = √3/2
    Or, sin(A + B) = sin 60°
    Or, A + B = 60° -------- (I)
    cos(A + 2B) = 1/2
    Or, cos(A + 2B) = cos 60°
    Or, A + 2B = 60° -------- (II)
    On solving 2 × equation I – equation II,
    We get, 2A + 2B − A − 2B = 120° − 60°
    Or, A = 60°
    Required value = tan(2A) = tan(120°) = -√3

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