In a triangle ABC, a (b cos C - c cos B) =

Options

A. `a^(2)`
B. `b^(2)-c^(2)`
C. 0
D. none of these

Explanation

To solve the problem \( a(b \cos C - c \cos B) \) in triangle \( ABC \), we will use the cosine rule and some algebraic manipulations.

### Step-by-Step Solution:

1. **Recall the Cosine Rule**:
The cosine rule states that for any triangle with sides \( a, b, c \) opposite to angles \( A, B, C \) respectively:
\[
b^2 = a^2 + c^2 - 2ac \cos B
...