By using the properties of definite integrals, evaluate the integrals`int_0^(pi/2) cos^2x dx`

Explanation

To evaluate the integral \(\int_0^{\frac{\pi}{2}} \cos^2 x \, dx\) using properties of definite integrals and trigonometric identities, we can follow these steps:

### Step 1: Use the Trigonometric Identity
We start by using the identity for \(\cos^2 x\):
\[ \cos^2 x = \frac{1 + \cos 2x}{2} \]
This allows us to rewrite the integral as:
...