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    Question

    If cosec (2A + B) = 1 and cosec (A + B) = (2/√3), find

    the value of (4A – B).
    A 120° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 90° Correct Answer Incorrect Answer
    D 60° Correct Answer Incorrect Answer

    Solution

    We have, cosec (2A + B) = 1

    Or, cosec (2A + B) = cosec 90°

    Or, 2A + B = 90° -------- (I)

    And, cosec (A + B) = (2/√3)

    Or, cosec (A + B) = cosec 60°

    Or, A + B = 60° ------- (II)

    On subtracting equation (II) from (I),

    We have, (2A + B) – (A + B) = 90° – 60°

    So, A = 30°

    Put the value of A = 30° in equation (II),

    So, 30° + B = 60°

    Or, B = 30°

    Therefore, required value = (4 × 30°) – 30° = 90°

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