Prove that `cos(pi/4+x)+cos(pi/4-x)=sqrt(2)cosx`.

Explanation

To prove that \( \cos\left(\frac{\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} - x\right) = \sqrt{2} \cos x \), we will start by expanding the left-hand side (LHS) using trigonometric identities.

### Step 1: Write down the LHS
\[ \text{LHS} = \cos\left(\frac{\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} - x\right) \]

### Step 2: Use the cosine addition and subtraction formulas
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