A fake smile is best used when around someone you hate. It can also be used to hide how sad you are; This definition is mostly used when in a crowded place (e.g) School, Party, A dinner, ect..
Nathan: Hi, how are you?
You: *Fake smile* Oh great, what about you?
the person with this name usually lives with a facade and often hides their sadness and only shows smiles on their face. They don't like to worry their loved ones and constantly go into the emo phase.
A fake smile is the most giga chad move when somebody starts shit up with you for the stupidest reasons
Some short hoe: *in a jeering voice* Hey dumbass, you parked your car in the wrong spot!
Me: *instead of wasting my time explaining why I parked there, I give a fake smile and walk away*
To deliver withering insults with a faux sweet smile. It's a socialized way for high ranking classy women/men who have to refrain from stooping to their haters level when in reality, they're desperately wishing that the person would be decapitated by a flying toilet carrying their own trots and any bullshit that the looseness of their bowels cannot carry.
A fake smile can also be used to replace the middle finger or a punch to the mouth to those who don't seem to understand that you could not care less of what they think of you. Their jealousy is a good indication that you must be an awesome person of the highest calibre to spark such fury, envy and outrage.