Question

    If cos(A - B) = √3/2 and cot(A + B) = 1/√3,

    where A - B and A + B are acute angles, then (2A - 3B) is equal to:
    A 30° Correct Answer Incorrect Answer
    B 45° Correct Answer Incorrect Answer
    C 60° Correct Answer Incorrect Answer
    D 15° Correct Answer Incorrect Answer

    Solution

    cos(A - B) = √ 3/2 A – B = 30˚ ---- (i) A + B = 60˚ ---- (ii) Solving (i) and (ii) we get, => A = 45˚ and B = 15˚ Now, => tan (2A – 3B) = 90˚ – 45˚ = 45˚

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