Here's an example: Imagine someone has just lost their job. They might "put on a brave face" when talking to their friends and family, pretending that everything is okay. But deep down, they are probably worried and anxious about the future.
Here are some synonyms for "put on a brave face":
* Fake it till you make it
* Keep up appearances
* Force a smile
* Grin and bear it
* Put on a front
Let me know if you'd like more examples or have any other questions!