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    Question

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

    then determine the value of (4A - B).
    A 15° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 45° Correct Answer Incorrect Answer
    D 60° Correct Answer Incorrect Answer

    Solution

    We have, cosec (2A + B) = (2/√3)

    Or, cosec (2A + B) = cosec 60°

    Or, 2A + B = 60° -------- (I)

    And, cosec (A + B) = √2

    Or, cosec (A + B) = cosec 45°

    Or, A + B = 45° ------- (II)

    On subtracting equation (II) from (I) ,

    We have, (2A + B) - (A + B) = 60° - 45°

    So, 'A' = 15°

    Put the value of 'A' = 15° in equation (1) ,

    So, 2(15°) + B = 60°

    Or, 30° + B = 60°

    So, 'B' = 30°

    Therefore, required value = (4 X 15) - 30 = 30°

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