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    Question

    If cosec (2A + B) = 2 and cosec (A + B) = 1, find the

    value of (3A – B).
    A 120° Correct Answer Incorrect Answer
    B 150° Correct Answer Incorrect Answer
    C 90° Correct Answer Incorrect Answer
    D 60° Correct Answer Incorrect Answer

    Solution

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

    Or, cosec (2A + B) = cosec 150°

    Or, 2A + B = 150° -------- (I)

    And, cosec (A + B) = 1

    Or, cosec (A + B) = cosec 90°

    Or, A + B = 90° ------- (II)

    On subtracting equation (II) from (I),

    We have, (2A + B) – (A + B) = 150° – 90°

    So, A = 60°

    Put the value of A = 60° in equation (II),

    So, 60° + B = 90°

    Or, B = 30°

    Therefore, required value = (3 × 60°) – 30° = 150°

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