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To speak while coughing. A noun or pronoun can be used between "cough" and "out." Although she tried to cough out her presentation, she ultimately had to stop and drink a glass of water.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
cough something out
to say something while coughing. He coughed the words out, but no one could understand him. He coughed out the name of his assailant.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.