The correct option is D a; no article
In expressing a comparison, if two nouns refer to the same person or thing, the article is used before the first noun only. But if the nouns refer to different persons or things, the article is used before each noun. SInce in the given statement, both the nouns dancer and singer refer to one person the article will be used before the first noun only and no article will be used before 'singer'. Also, the indefinite article 'a' should be used whenever someone's work or job is being referred to. Therefore Option D is the correct answer. Since the nouns are not used to refer the different type of work she does, the indefinite article 'a' cannot be used before the second noun' singer'. Therefore, Option A is incorrect. 'The' cannot be used in when the nouns are being used in general sense to single out an individual as the representative of a class. Therefore, Option B and C are incorrect.