For any triangle ABC, prove that`a(bcosC-c cosB)=b^2-c^2`

Explanation

To prove the equation \( a(b \cos C - c \cos B) = b^2 - c^2 \) for any triangle \( ABC \), we will use the cosine rule.

### Step-by-Step Solution:

1. **Write down the cosine rule**:
The cosine rule states that for any triangle \( ABC \):
\[
\cos A = \frac{b^2 + c^2 - a^2}{2bc}, \quad \cos B = \frac{a^2 + c^2 - b^2}{2ac}, \quad \cos C = \frac{a^2 + b^2 - c^2}{2ab}
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