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

Explanation

To prove that \( a(b \cos C - c \cos B) = b^2 - c^2 \) for any triangle ABC, we will follow these steps:

### Step 1: Use the Law of Cosines
We start by recalling the Law of Cosines, which states:
\[ a^2 = b^2 + c^2 - 2bc \cos A \]
We can express \( a \) in terms of \( b \) and \( c \):
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