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    Question

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

    value of (3A тАУ 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) тАУ (A + B) = 150┬░ тАУ 90┬░

    So, A = 60┬░

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

    So, 60┬░ + B = 90┬░

    Or, B = 30┬░

    Therefore, required value = (3 ├Ч 60┬░) тАУ 30┬░ = 150┬░

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