In ` A B C ,` if `A B=c` is fixed, and `cosA+cosB+2cos C=2` then the locus of vertex `C` is ellipse (b) hyperbola (c) circle (d) parabola

Explanation

To solve the problem, we need to analyze the given equation and determine the locus of vertex C in triangle ABC, where AB is fixed and \( \cos A + \cos B + 2 \cos C = 2 \).

### Step-by-step Solution:

1. **Start with the given equation:**
\[ \cos A + \cos B + 2 \cos C = 2 \]
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