\[\sin{130{^\circ}} + \sin{10{^\circ}} =\]
\[= 2\sin\frac{140{^\circ}}{2} \cdot \cos\frac{120{^\circ}}{2} =\]
\[= 2\sin{70{^\circ}} \cdot \cos{60{^\circ}} =\]
\[= 2\sin{70{^\circ}} \cdot \frac{1}{2} = \sin{70{^\circ}\ }\]