Answer
$\dfrac{1}{2}$
Work Step by Step
Recall:
$\cos(\alpha-\beta)=\cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$
Hence,
$\cos(80^\circ)\cos(20^\circ)+\sin(80^\circ)\sin(20^\circ)\\
=\cos(80^\circ-20^\circ)\\
=\cos(60^\circ)\\
=\frac{1}{2}$
