Prove that: \[ \frac{\sin 5 x+\sin 3 x}{\cos 5 x+\cos 3 x}=\tan 4 x \]

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Prove that:
\[
\frac{\sin 5 x+\sin 3 x}{\cos 5 x+\cos 3 x}=\tan 4 x
\]
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