If you've been sneaking around with your best friend's boyfriend, that's probably one secret you don't want to divulge, because revealing that tidbit of information will probably cut your friendship short.
Divulge often precedes the word secret, because it means to reveal something, and that something is often of a personal or private nature. A gossip columnist's job is to divulge which celebrities are secretly dating and which ones have been caught in embarrassing situations. Although the word comes from the Latin word for making something public to the masses, it can also be used to describe information passed from one person to another. For example, a mother could divulge to her daughter that she was adopted.