Answer
$2$
Work Step by Step
$y=\cos^{-1}x$ is the number in $[0, \pi]$ for which $\cos y=x.$
Since $\displaystyle \cos\frac{\pi}{3}=\frac{1}{2}$, it follows that $\displaystyle \cos^{-1}\frac{1}{2}=\frac{\pi}{3}.$
$\displaystyle \sec(\cos^{-1}\frac{1}{2})=\sec\frac{\pi}{3}$
$=\displaystyle \frac{1}{\cos\frac{\pi}{3}}$
$=\displaystyle \frac{1}{\frac{1}{2}}=2$
