1. **State the problem:** Simplify the expression $\sec(x) + \cos(x)$. 2. **Recall the definitions:** $\sec(x) = \frac{1}{\cos(x)}$. 3. **Rewrite the expression using this definition:** $$\sec(x) + \cos(x) = \frac{1}{\cos(x)} + \cos(x)$$ 4. **Find a common denominator to combine the terms:** $$\frac{1}{\cos(x)} + \cos(x) = \frac{1}{\cos(x)} + \frac{\cos^2(x)}{\cos(x)} = \frac{1 + \cos^2(x)}{\cos(x)}$$ 5. **Final simplified form:** $$\boxed{\frac{1 + \cos^2(x)}{\cos(x)}}$$ This is the simplest form unless further context or constraints are given.