Prove that: \[ \frac{1+\sin 2 x-\cos 2 x}{1+\sin 2 x+\cos 2 x}=\tan x \]

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Prove that:
\[
\frac{1+\sin 2 x-\cos 2 x}{1+\sin 2 x+\cos 2 x}=\tan x
\]
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