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Prove that: cos((3pi)/4+x)-cos((3pi)/4-x...

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

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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 subtraction formula. ### Step-by-step Solution: 1. **Identify the Left-Hand Side (LHS)**: \[ \text{LHS} = \cos\left(\frac{3\pi}{4} + x\right) - \cos\left(\frac{3\pi}{4} - x\right) \] ...
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