Why did hortensia and lucentio claim to be litio and cambio?

Hortensio and Lucentio claimed to be Litio and Cambio, respectively, to disguise their true identities while pursuing their romantic interests in "The Taming of the Shrew." Lucentio, in his guise as Cambio, sought to woo Bianca, while Hortensio, as Litio, aimed to gain Bianca's affection as well. Their assumptions of these identities allowed them to navigate the complexities of courtship without revealing their true intentions, ultimately adding layers of deception and comedic tension to the play.