Prove that `cosA+cosB+cosC=1+r/R`

Explanation

To prove that \( \cos A + \cos B + \cos C = 1 + \frac{r}{R} \), where \( A, B, C \) are the angles of a triangle, \( r \) is the inradius, and \( R \) is the circumradius, we can follow these steps:

### Step 1: Use the formula for the sum of cosines in a triangle
We start with the known identity for the sum of cosines in a triangle:
\[ \cos A + \cos B + \cos C = 1 + \frac{r}{R} \]
This is a well-known result in triangle geometry.
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