Making a loud, bragging announcement; also literally playing a trumpet or making the loud sound an elephant makes.
From 'trumpet' (the brass instrument, from Old French 'trompette'). The verb form developed from the instrument's loud sound, becoming metaphorical for loud announcements and also describing animal calls.
Elephants actually do 'trumpet' as a form of communication—the sound can travel miles and means different things (greeting, distress, anger)—so calling someone 'trumpeting' their success compares them to a 5-ton animal making noise!
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