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      Question

      If sin (2A − 3B) = (1/2) and cos (A + B) = (√3/2),

      where 0° < A, B < 90°, then find the value of ‘A’.
      A 24° Correct Answer Incorrect Answer
      B 30° Correct Answer Incorrect Answer
      C 36° Correct Answer Incorrect Answer
      D 18° Correct Answer Incorrect Answer

      Solution

      sin (2A − 3B) = (1/2)
      Or, sin (2A − 3B) = sin 30°
      Or, 2A − 3B = 30° ----------- (I)

      And, cos (A + B) = (√3/2)
      Or, cos (A + B) = cos 30°
      Or, A + B = 30° -------------- (II)

      On solving equation I + 3 × equation II, we get;
      2A − 3B + 3 × (A + B) = 30 + 3 × 30
      Or, 2A − 3B + 3A + 3B = 120°
      Or, 5A = 120°
      So, ‘A’ = 24°

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