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 can use the cosine subtraction formula.

### Step-by-Step Solution:

1. **Identify the expression**:
We start with the expression \( \cos\left(\frac{3\pi}{4} + x\right) - \cos\left(\frac{3\pi}{4} - x\right) \).

2. **Use the cosine subtraction formula**:
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