Докажите равенство sin200°+sin100°=sin40°.

\[\sin{200{^\circ}} + \sin{100{^\circ}} = \sin{40{^\circ}}\]

\[2\sin\frac{300{^\circ}}{2} \cdot \cos\frac{100{^\circ}}{2} = \sin{40{^\circ}}\]

\[2\sin{150{^\circ}} \cdot \cos{50{^\circ}} = \sin{40{^\circ}}\]

\[2\sin\left( \frac{\pi}{2} + 60{^\circ} \right) \cdot \cos\left( \frac{\pi}{2} - 40{^\circ} \right) =\]

\[= \sin{40{^\circ}}\]

\[2\cos{60{^\circ}} \cdot \sin{40{^\circ}} = \sin{40{^\circ}}\]

\[2 \cdot \frac{1}{2} \cdot \sin{40{^\circ}} = \sin{40{^\circ}}\]

\[\sin{40{^\circ}} = \sin{40{^\circ}}\]