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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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