Let $a$ and $b$ be angles such that
\[\cos (a + b) = \cos a + \cos b.\]Find the maximum value of $\cos a.$
Question:
Let $a$ and $b$ be angles such that
\[\cos (a + b) = \cos a + \cos b.\]Find the maximum value of $\cos a.$
Answer:
Let's think step by step.

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\sqrt{3} - 1
Let $a$ and $b$ be angles such that
\[\cos (a + b) = \cos a + \cos b.\]Find the maximum value of $\cos a.$
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