In a triangle ABC, 2ac sin`((A-B+C)/2)` =

Options

A. `a^(2)+b^(2)-c^(2)`
B. `c^(2)+a^(2)-b^(2)`
C. `b^(2)-c^(2)-a^(2)`
D. `c^(2)-a^(2)-b^(2)`

Explanation

To solve the problem, we need to find the value of \( 2ac \sin\left(\frac{A - B + C}{2}\right) \) in triangle \( ABC \).

### Step-by-Step Solution:

1. **Identify the Expression**: We start with the expression \( 2ac \sin\left(\frac{A - B + C}{2}\right) \).

2. **Use the Angle Sum Property**: We know that the sum of angles in a triangle is \( A + B + C = \pi \). Therefore, we can express \( A + C \) in terms of \( B \):
\[
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