How does Don Pasquale discover that Sofronia is really Norina?

In Gaetano Donizetti’s opera Don Pasquale, the protagonist does not discover that his wife, "Sofronia," is actually Norina until the very end of the story.1

Throughout the plot, Don Pasquale is deceived by Dr. Malatesta, who orchestrates a fake marriage between the elderly bachelor and Norina, who is disguised as Malatesta’s shy sister, "Sofronia". Pasquale remains unaware of the ruse even as his "wife" makes his life miserable.12

The revelation occurs in the final scene of Act III in a garden near Pasquale’s house. After Pasquale attempts to catch "Sofronia" in an act of infidelity, Malatesta intervenes to resolve the conflict. He tells "Sofronia" that Norina—Ernesto’s betrothed—will be moving into the house. When "Sofronia" expresses outrage and demands to leave, Malatesta suggests that Pasquale should allow Ernesto to marry Norina immediately so that "Sofronia" will consent to vacate the premises.1

When Ernesto arrives, Malatesta finally reveals to the stunned Don Pasquale that the woman he married was never his sister, but rather Norina in disguise, and that the marriage was a trick.1