Answer
$1$
Work Step by Step
Function Values of Special Angles$: $
$\displaystyle \cos 60^{o}=\frac{1}{2}, \quad \sin 30^{o}=\frac{1}{2}$
$\displaystyle \cos 60^{\mathrm{o}}+2\sin^{2}30^{\mathrm{o}}=\frac{1}{2}+2(\frac{1}{2})^{2}$
$=\displaystyle \frac{1}{2}+2(\frac{1}{4})$
$=\displaystyle \frac{1}{2}+\frac{1}{2}=1$