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      Question

      If sin (4A − B) = (√2/2) and cos (A + B) = (√2/2),

      where 0° < A, B < 90°, then find the value of ‘A’.
      A 18° Correct Answer Incorrect Answer
      B 24° Correct Answer Incorrect Answer
      C 30° Correct Answer Incorrect Answer
      D 12° Correct Answer Incorrect Answer

      Solution

      sin (4A − B) = (√2/2)
      Or, sin (4A − B) = sin 45°
      Or, 4A − B = 45° ----------- (I)

      And, cos (A + B) = (√2/2)
      Or, cos (A + B) = cos 45°
      Or, A + B = 45° -------------- (II)

      On solving equation I + 1 × equation II, we get;
      4A − B + (A + B) = 45 + 45
      Or, 5A = 90°
      So, ‘A’ = 18°

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