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      Question

      If cosec (2A + B) = 1 and cosec (A + B) = (2/√3), find

      the value of (4A – B).
      A 120° Correct Answer Incorrect Answer
      B 30° Correct Answer Incorrect Answer
      C 90° Correct Answer Incorrect Answer
      D 60° Correct Answer Incorrect Answer

      Solution

      We have, cosec (2A + B) = 1

      Or, cosec (2A + B) = cosec 90°

      Or, 2A + B = 90° -------- (I)

      And, cosec (A + B) = (2/√3)

      Or, cosec (A + B) = cosec 60°

      Or, A + B = 60° ------- (II)

      On subtracting equation (II) from (I),

      We have, (2A + B) – (A + B) = 90° – 60°

      So, A = 30°

      Put the value of A = 30° in equation (II),

      So, 30° + B = 60°

      Or, B = 30°

      Therefore, required value = (4 × 30°) – 30° = 90°

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