From Longman Dictionary of Contemporary Englishnose something ↔ out phrasal verb informal1 FIND OUTto discover some information that someone else does not want you to discover The media always manage to nose out some interesting facts about a politician’s past life.2 to defeat someone by a very small amount in a race, competition etc → nose→ See Verb table
Examples from the Corpus
nose out• His nose can smell out a human or a Minpin or any other animal from ten miles away.• The nose probably started out fairly small, like that of, say, the modern tapir.• Breathe in through the nose and out hard through the mouth, both to a slow count of four.• Rumpipumpy nosed Gastronomical out of third.• Breathe in through your nose and out through your mouth.• The nose, dried out, was pitifully thin and pinched. 