Evaluate the definite integrals`int_0^(pi/2)cos^2xdx`

Explanation

To evaluate the definite integral \( \int_0^{\frac{\pi}{2}} \cos^2 x \, dx \), we can follow these steps:

### Step 1: Use the identity for \( \cos^2 x \)
We know the trigonometric identity:
\[ \cos^2 x = \frac{1 + \cos 2x}{2} \]
Using this identity, we can rewrite the integral:
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