By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{\Large 2}\cos^2x\;dx \end{align*}$

Question

$\begin{array}{1 1} \frac{\pi}{4} \\ \frac {\pi}{2} \\ \frac{\pi}{8} \\ \frac{\pi}{16} \end{array} $