Answer with Explanation:
Othello acted calmly and wasn't worried about people looking for him. Since he really loves "Desdemona," the senator's daughter, and he had a very good service record as a general Venetian army, then he thought it would get him through.
When Othello was taken to the duke, he defended himself for he was about to be killed. The duke listened to his story that he didn't use any magic spells in order to attract Desdemona. The story was confirmed when Desdemona arrived. There was, indeed, no trickster involved and both of them (Othello and Desdemona) were actually in love and were married. So, this dismissed the claim of Brabanzio, the father of Desdemona.