In a triangle ABC, 2ac sin 1/2 (A – B + C) =
(A) a2+b2-c2 (B) c2+a2-b2
(C) b2-c2-a2 (D) c2-a2-b2

A+B+C=Pi

so A+C = Pi - B

so here it will be :  2ac.sin(Pi/2 -B) = 2ac.cosB

by cosine rule, we have: c²+a²-b² = 2ac cos B

option B

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Ramesh 
IIT Kgp - 05 batch