The police made the suspect 'cough up' the names of his accomplices.
They 'coughed up' [='lost, gave up'] the lead in the second half.
We had to 'cough up' an extra hundred dollars for the car rental.
(..) Narrator: The new black hole in the middle Keeps feeding on the body of the star around it. It eats the gas so fast, it chokes and coughs, Blasting out huge beams of energy. Dr. Plait: They basically eat their way out from the star. This happens in milliseconds. (..)2010 TvShow: How the Universe Works Title: Black Holes Season: 1 Episode 2