question from act 3
Lucentio and Hortensio, disguised respectively as Cambio and Litio, vie for the attention of the fair Bianca. Bianca seems thoroughly amused by the competition, and decides that Lucentio may lecture her while Hortensio tunes his lute; once the instrument is in tune, Hortensio may then take over the lesson. Lucentio leaps into action with his "lesson," confessing his identity and his love under the guise of a Latin translation. Bianca responds with her own variant of the game, telling him, through her own "translation," that she does not know him and cannot trust him - but that he should "despair not." (3.1: 44) Hortensio fares less well than Lucentio when he tries to confess his love through a scale on the lute. Bianca dismisses the rouse and all but Hortensio exit at a servant's bidding to help prepare Katharina's room for her wedding tomorrow. Alone on stage, Hortensio notes that Cambio appeared to be courting Bianca, and declares that if Bianca is unable to be faithful to him, he won't be faithful to her either. Yes, they are aware each other is competing for her affections.
http://www.gradesaver.com/the-taming-of-the-shrew/study-guide/section4/
