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    Question

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

    find the value of (4A - B) .
    A 15° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 60° Correct Answer Incorrect Answer
    D 40° Correct Answer Incorrect Answer

    Solution

    We have, cosec (2A + B) = (2/√3)
    Or, cosec (2A + B) = cosec 60o

    Or, 2A + B = 60o -------- (I)

    And, cosec (A + B) = √2

    Or, cosec (A + B) = cosec 45o

    Or, A + B = 45o ------- (II)

    On subtracting equation (II) from (I) ,

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

    So, 'A' = 15o

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

    So, 2(15o) + B = 60o

    Or, 30o + B = 60o

    So, 'B' = 30o

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

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