Integrate the functions`(cos2x-cos2alpha)/(cosx-cosalpha)`

Explanation

To solve the integral \( I = \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \), we will follow these steps:

### Step 1: Rewrite the numerator using trigonometric identities
We can use the identity for cosine of double angles:
\[ \cos 2x = 2\cos^2 x - 1 \quad \text{and} \quad \cos 2\alpha = 2\cos^2 \alpha - 1 \]
Substituting these into the integral gives:
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