To evaluate the integral \( \int \frac{1 - \cos x}{1 + \cos x} \, dx \), we will follow these steps:
### Step 1: Rewrite the integrand using trigonometric identities
We know the following trigonometric identities:
\[
1 - \cos x = 2 \sin^2 \left(\frac{x}{2}\right)
\]
\[
...