Prove that: `cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx`

Explanation

To prove that \( \cos\left(\frac{3\pi}{4} + x\right) - \cos\left(\frac{3\pi}{4} - x\right) = \sqrt{2} \sin x \), we will use the cosine addition and subtraction formulas.

### Step-by-Step Solution:

1. **Apply the Cosine Addition Formula**:
\[ \cos\left(\frac{3\pi}{4} + x\right) = \cos\left(\frac{3\pi}{4}\right)\cos(x) - \sin\left(\frac{3\pi}{4}\right)\sin(x) \]
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