Докажите равенство cos140°+cos80°=-(корень из 3)sin20°.

\[\cos{140{^\circ}} + \cos{80{^\circ}} = - \sqrt{3}\sin{20{^\circ}}\]

\[2\cos{110{^\circ}} \cdot \frac{\sqrt{3}}{2} = - \sqrt{3}\sin{20{^\circ}}\]

\[\sqrt{3} \cdot \cos\left( \frac{\pi}{2} + 20{^\circ} \right) = - \sqrt{3}\sin{20{^\circ}}\]

\[- \sqrt{3}\sin{20{^\circ}} = - \sqrt{3}\sin{20{^\circ}}\]