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      Question

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

      value of (3A – 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) – (A + B) = 150° – 90°

      So, A = 60°

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

      So, 60° + B = 90°

      Or, B = 30°

      Therefore, required value = (3 × 60°) – 30° = 150°

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