Prove that \[ \cos x \cos \frac{x}{2}-\cos 3 x \cos \frac{9 x}{2}=\sin 4 x \sin \frac{7 x}{2} \]
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Prove that
\[
\cos x \cos \frac{x}{2}-\cos 3 x \cos \frac{9 x}{2}=\sin 4 x \sin \frac{7 x}{2}
\]
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