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    Question

    If sin (3A − 4B) = (1/2) and cos (A + B) = (√2/2),

    where 0° < A, B < 90°, then find the value of ‘A’.
    A 30° Correct Answer Incorrect Answer
    B 40° Correct Answer Incorrect Answer
    C 20° Correct Answer Incorrect Answer
    D 15° Correct Answer Incorrect Answer

    Solution

    sin (3A − 4B) = (1/2)
    Or, sin (3A − 4B) = sin 30°
    Or, 3A − 4B = 30° ----------- (I)

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

    On solving equation I + 4 × equation II, we get;
    3A − 4B + 4 × (A + B) = 30 + 4 × 45
    Or, 3A − 4B + 4A + 4B = 210°
    Or, 7A = 210°
    So, ‘A’ = 30°

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