Evaluate the definite integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{2}\cos^2xdx \end{align*}$

Question

$\begin{array}{1 1}\large \frac{\pi}{4} \\\large \frac{\pi}{2} \\ \large \frac{\pi}{6} \\ \large \frac{\pi}{8} \end{array} $