Answer
$\frac{1}{2}$
Work Step by Step
To find exact value of $\cos 420^{\circ}$, let's find its co-terminal angle between $0^{\circ}$ and $360^{\circ}$ first-
Co-terminal angle of $420^{\circ}$ = $420^{\circ} - 360^{\circ}$ = $60^{\circ}$
Therefore
$\cos 390^{\circ}$ = $\cos 60^{\circ}$
($60^{\circ}$ and $420^{\circ}$ are co-terminal and trigonometric functions of co-terminal angles are same)
As $ 420^{\circ}$ terminates in quadrant I, its $\cos$ will be positive.
Therefore-
$\cos 420^{\circ}$ = $\cos 60^{\circ}$ = $\frac{1}{2}$
