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

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