Answer
$2$
Work Step by Step
$\sec{(\theta+ 360^{\circ} k)} = \sec{\theta}$
$\therefore \sec{420^{\circ}} = \sec{(60^{\circ}+360^{\circ})} = \sec{60^{\circ}}$
$\sec{60^{\circ}} = \dfrac{1}{\cos{60^{\circ}}}=\dfrac{1}{\frac{1}{2}}=\boxed{2}$
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