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    Question

    If sin (4A − 5B) = (√2/2) and cos (A + B) = (√2/2),

    where 0° < A, B < 90°, then find the value of ‘A’.
    A 30° Correct Answer Incorrect Answer
    B 25° Correct Answer Incorrect Answer
    C 35° Correct Answer Incorrect Answer
    D 20° Correct Answer Incorrect Answer

    Solution

    sin (4A − 5B) = (√2/2)
    Or, sin (4A − 5B) = sin 45°
    Or, 4A − 5B = 45° ----------- (I)

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

    On solving equation I + 5 × equation II, we get;
    4A − 5B + 5 × (A + B) = 45 + 5 × 45
    Or, 4A − 5B + 5A + 5B = 270°
    Or, 9A = 270°
    So, ‘A’ = 30°

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