From Longman Dictionary of Contemporary Englishsweat something ↔ out phrasal verb1 to wait anxiously for news that is very important to you Charles is sweating it out while the coach decides which players he’s taking to the Olympics.2 American English to work very hard on something, especially something difficult kids sweating out a test3 to do hard physical exercise They were sweating it out in the gym.4 MIto get rid of an illness by making yourself sweat a lot → sweat→ See Verb table
Examples from the Corpus
sweat out• The men believe in fiat stomach muscles and sweating things out.• Two of the men were in shirts, sweating, pounding out beer after beer.• I sweated it out for maybe two or three minutes without making a move.• Jessica felt sweat break out fresh on her skin as they walked in.• Even so, if you grit your teeth and sweat it out, most of them do emerge as reasonable human beings.• She grunted until sweat stood out on her brow.• His eyes are popping and sweat stands out on his skin.• He lives with them every day, and sweats them out on many a sleepless night.From Longman Business Dictionarysweat something → out phrasal verb [transitive] to continue doing something that has been started, even though it is very difficult or worryingCompanies that have taken the plunge to the private sector must sweat out low returns in the hope that they can return to profit.We had a slow start-up in the business, but we were determined tosweat it out. → sweat→ See Verb table 