Answer
$\dfrac{\sqrt2}{2}$
Work Step by Step
Recall:
$\cos(\alpha-\beta)=\cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$.
Hence,
$\cos(65^\circ)\cos(20^\circ)+\sin(65^\circ)\sin(20^\circ)\\
=\cos(65^\circ-20^\circ)\\
=\cos(45^\circ)\\
=\frac{\sqrt2}{2}$
