In `Delta ABC`, prove that `c cos (A - alpha) + a cos (C + alpha) = b cos alpha`

Explanation

To prove that \( c \cos(A - \alpha) + a \cos(C + \alpha) = b \cos \alpha \) in triangle \( \Delta ABC \), we will start with the left-hand side (LHS) and manipulate it step by step.

### Step 1: Write down the left-hand side
\[ \text{LHS} = c \cos(A - \alpha) + a \cos(C + \alpha) \]

### Step 2: Apply the cosine angle subtraction and addition formulas
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