Докажите равенство sin160°-sin100°=-cos50°.

\[\sin{160{^\circ}} - \sin{100{^\circ}} = - \cos{50{^\circ}}\]

\[2\sin\frac{60{^\circ}}{2} \cdot \cos\frac{260{^\circ}}{2} = - \cos{50{^\circ}}\]

\[2\sin{30{^\circ}} \cdot \cos{130{^\circ}} = - \cos{50{^\circ}}\]

\[2 \cdot \frac{1}{2} \cdot \cos{(\pi - 50{^\circ})} = - \cos{50{^\circ}}\]

\[- \cos{50{^\circ}} = - \cos{50{^\circ}}\]