Show that: \[ \sin 50^{\circ} \cos 85^{\circ}=\frac{1-\sqrt{2} \sin 35^{\circ}}{2 \sqrt{2}} \]

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Show that:
\[
\sin 50^{\circ} \cos 85^{\circ}=\frac{1-\sqrt{2} \sin 35^{\circ}}{2 \sqrt{2}}
\]
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