Prove that \[ \frac{(\sin 7 x+\sin 5 x)+(\sin 9 x+\sin 3 x)}{(\cos ...

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Prove that
\[
\frac{(\sin 7 x+\sin 5 x)+(\sin 9 x+\sin 3 x)}{(\cos 7 x+\cos 5 x)+(\cos 9 x+\cos 3 x)}=\tan 6 x
\]
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