In triangle \( A B C, 2 a c \sin \left(\frac{1}{2}(A-B+C)\right) \) is equal to (A) \( a^{2}+b^{...

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In triangle \( A B C, 2 a c \sin \left(\frac{1}{2}(A-B+C)\right) \) is equal to
(A) \( a^{2}+b^{2}-c^{2} \)
(B) \( b^{2}-c^{2}-a^{2} \)
(C) \( c^{2}+a^{2}-b^{2} \)
(D) \( c^{2}-a^{2}-b^{2} \)
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