Answer
$\dfrac{1}{2}$
Work Step by Step
Note that $\sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$.
Hence,
$\sin(20^\circ)\cos(10^\circ)+\cos(10^\circ)\sin(20^\circ)\\
=\sin(20^\circ+10^\circ)\\
=\sin(30^\circ)\\
=\frac{1}{2}$