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2ac sin((A - B + C)/2) in terms of the sides

The same question, asked 2 times: 16 May 2023 S1, 14 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S1

    103
    In a triangle ABC, with usual notations, 2acsin⁡ ⁣(A−B+C2)2ac\sin\!\left(\frac{A-B+C}{2}\right) is equal to

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  2. Question 2

    14 May 2024 S1

    147
    In △ABC\triangle ABC, with usual notations, 2acsin⁡12(A−B+C)2ac\sin\dfrac{1}{2}(A-B+C) is equal to

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