As a Danish person I would never say "manden er en vegetar" with the article "en". I would say "manden er vegetar" in the same way I would say "manden er far" for someone who is a father. If the sentence continued and said "the man is a vegetarian who misses bacon" I would say "manden er en vegetar, som savner bacon". (in the example using a father it could be "the man is a father who loves his children" - "manden er en far, som elsker sine børn".)
I got the question right, but I was curious about the phrasing.
Based upon a previous phrasing and what I know of Swedish and Norwegian, I thought that the indefinite article was typically dropped in phrases denoting "occupation".
Is it an optional construct?
A previous lesson had us translating "Manden er vegetar" from Danish. Other example from Norwegian: "Han er student".