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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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