"Taming of the Shrew": did Kate perform a REAL transformation?

In the end of the book "The taming of the Shrew" originally written by William Shakespeare, Kate seems at have been tamed of her wild attitude at the end of the book. After she kisses her husband, he feels as if she has been transformed. Although people have the power to change their behavior, I believe that Katharine was faking her change.
I think she faked her change, because she wanted to embarrass her sister, Bianca. At a wedding, Bianca was mean and didn't want to come out to see the wedding. Her sister Katherine went and forced her to come out and see it. She told Bianca to be a goo…