You don't need another definite article before baker. This one marks it incorrect in error.
This is how I see it: The definite article is needed because otherwise it would be one person "the cook and baker". This, however, is ruled out by the verb being the plural form "coquunt".
Since these are two people, two definite articles are required. I'm not a native speaker of English or Latin ;-), though. So let's wait for other opinions.