Answer
$\sqrt3$
Work Step by Step
$\cot \alpha =\cot \left( \alpha -360^o\right)
\\\Rightarrow \cot 390^o=\cot \left( 390^o-360^o\right)
\\=\cot 30^o
\\=\dfrac {\cos 30^o}{\sin 30^o}
\\=\dfrac {\cos \dfrac {\pi }{6}}{\sin \dfrac {\pi }{6}}
\\=\dfrac {\dfrac {\sqrt {3}}{2}}{\dfrac {1}{2}}
\\=\sqrt {3}$