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 can use the cosine addition and subtraction formulas.

### Step-by-Step Solution:

1. **Write down the cosine addition and subtraction formulas**:
\[ \cos(a + b) = \cos a \cos b - \sin a \sin b \]
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