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 use the sum-to-product identities in trigonometry.

### Step-by-Step Solution:

1. **Identify the expression**:
We start with the left-hand side of the equation:
\[
LHS = \cos\left(\frac{\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} - x\right)
...