As "American Hustle" builds toward its climax, Rosalyn (Jennifer Lawrence) sees Edith (Amy Adams) for the first time and instantly recognizes Edith as Rosalyn's husband's mistress.
How did Rosalyn know who Edith was?
Rosalyn knew that her husband wanted to leave her but kept manipulating him back. From this I assume she knew he had a mistress. She guessed from his reaction when he saw her walking through the smoke.