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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 the identity \( \cos\left(\frac{3\pi}{4} + x\right) - \cos\left(\frac{3\pi}{4} - x\right) = -\sqrt{2} \sin x \), we will start with the left-hand side and simplify it step by step. ### Step 1: Write down the left-hand side We start with the expression: \[ LHS = \cos\left(\frac{3\pi}{4} + x\right) - \cos\left(\frac{3\pi}{4} - x\right) \] ...
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