The difference between to discover and to find out is a fine one.
Use the verb to discover to talk about information and things that are completely new. You can also use discover if you are the first person to learn some new information.
- Captain Cook discovered Antarctica.
- Sir Alexander Fleming discovered Penicillin when he forgot to clean up his work bench.
- She found out she was pregnant at the doctor’s office.
- I’ve found out how to make the perfect chocolate cookies.
- You will never find out my secret.
Find out has an additional meaning. It can be used to describe a situation when somebody is caught doing something that they shouldn’t.
- The students tried to cheat in the exam but they were found out.
- People who lie and steal are invariably found out in the end.
Uncover has quite a different meaning. We use this verb as synonym of to reveal information. It is also used in a literal way when a lid, cap, or other form is covering is removed.
- She uncovered her shoulders and revealed her tattoos.
- The evidence was uncovered when one of the accused told everything to the police.