Dokaži da je zbroj cos3∘cos6∘−cos2∘+cos5∘cos10∘−cos2∘+⋯+cos(2n+1)∘cos(4n+2)∘−cos2∘+⋯+cos89∘cos178∘−cos2∘\frac{\cos 3^\circ}{\cos 6^\circ - \cos 2^\circ} + \frac{\cos 5^\circ}{\cos 10^\circ - \cos 2^\circ} + \cdots + \frac{\cos(2n + 1)^\circ}{\cos(4n + 2)^\circ - \cos 2^\circ} + \cdots + \frac{\cos 89^\circ}{\cos 178^\circ - \cos 2^\circ}cos6∘−cos2∘cos3∘+cos10∘−cos2∘cos5∘+⋯+cos(4n+2)∘−cos2∘cos(2n+1)∘+⋯+cos178∘−cos2∘cos89∘ jednak sin2∘−14sin1∘⋅sin2∘.\frac{\sin 2^\circ - 1}{4 \sin 1^\circ \cdot \sin 2^\circ}.4sin1∘⋅sin2∘sin2∘−1.