Which article is appropriate in the blank below, a or the?
— What are you singing? I've heard the song many times.
— This is __ song by Lady Gaga.
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Either one can be used, depending on what you are trying to say.
I'd probably use the word "the" only if I was talking about Lada Gaga's latest hit, one that was getting a lot of airplay on the radio. That would be a shortened way of saying:
If it was one of her former hits, though, like Poker Face or Bad Romance, then I'd almost certainly use a instead of the.
I’m not even sure you need to worry about whether it should be the song, that song or this song. I think I would simply use this: