Answer
$2$
Work Step by Step
$\sec{\alpha} =\sec{\left( \alpha -360^o\right)}
\\\Rightarrow \sec{420^o}=\sec{\left( 420^o-360^o\right)}
\\=\sec{60^o}
\\=\dfrac {1}{\cos 60^o}
\\=\dfrac {1}{\cos \dfrac {\pi }{3}}
\\=\dfrac {1}{\frac {1}{2}}
\\=2$
