`(cos x)/(cos (x+a))`

Explanation

To solve the integral \( \int \frac{\cos x}{\cos(x + a)} \, dx \), we can follow these steps:

### Step 1: Rewrite the integrand
We can rewrite the integrand by adding and subtracting \( \cos a \) in the numerator:
\[ \frac{\cos x}{\cos(x + a)} = \frac{\cos x + \cos a - \cos a}{\cos(x + a)} = \frac{\cos x + \cos a}{\cos(x + a)} - \frac{\cos a}{\cos(x + a)} \]

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