Voting to close and adding your new answer to the more general master question is definitely good, but pasting the exact same answer below the duplicate question is unnecessary at the very least.
It could even be considered abusive if someone repeatedly posts the same answer in multiple locations, because that might be a cheap way to harvest reputation with few effort and contribution. The system actually raises an automatic moderator flag on completely identical posts. If it's a rare occurrence and does not involve low quality posts, most likely there will be no action taken though.
Anyway, it would be fine and welcome if you adapt your answer on the duplicate post and tailor it to the specifics of the question, while still voting to close it as duplicate of the a more general question. However, if there is nothing to adapt, better just post on the master question and maybe leave a comment on the to-be-closed duplicate that links to your answer and briefly explains why you think it suits the question best.