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In triangle \( A B C, a, b, c \) are the lengths of its sides and \( A \), \( B, C \) are the angles of triangle \( A B C \). The correct relation is given by
(A) \( (b-c) \sin \left(\frac{B-C}{2}\right)=a \cos \frac{A}{2} \)
(B) \( (b-c) \cos \left(\frac{A}{2}\right)=a \sin \frac{B-C}{2} \)
(C) \( (b+c) \sin \left(\frac{B+C}{2}\right)=a \cos \frac{A}{2} \)
(D) \( (b-c) \cos \left(\frac{A}{2}\right)=2 a \sin \frac{B+C}{2} \)
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