Prove that: \[ \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)=\frac{1}{2} \...

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Prove that:
\[
\sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)=\frac{1}{2} \cos 2 x
\]
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