Prove that: \[ \frac{\sin 5 x+2 \sin 8 x+\sin 11 x}{\sin 8 x+2 \sin 11 x+\sin 14 x}=\frac{\sin 8...

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Prove that:
\[
\frac{\sin 5 x+2 \sin 8 x+\sin 11 x}{\sin 8 x+2 \sin 11 x+\sin 14 x}=\frac{\sin 8 x}{\sin 11 x}
\]
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