Question

    If sin(A + B) = 1/2 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 1/√3 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D 2 Correct Answer Incorrect Answer

    Solution

    sin(A + B) = 1/2
    Or, sin(A + B) = sin 30°
    Or, A + B = 30° -------- (I)
    cos(A + 2B) = 1/√2
    Or, cos(A + 2B) = cos 45°
    Or, A + 2B = 45° -------- (II)
    On solving 2 × equation I – equation II,
    We get, 2A + 2B − A − 2B = 60° − 45°
    Or, A = 15°
    Required value = tan(2A) = tan(30°) = 1/√3

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