Answer:
a. Cognitive Dissonance Theory
Step-by-step explanation:
In psychology, the term cognitive dissonance refers to the stress that a person experiences when he/she faces contradictory beliefs, ideas or values or when he/she has to act in a way that is contrary to these beliefs, ideas or values. In order to reduce the stress that this behavior generates, the person starts having thoughts that will reduce the stress and starts convincing himself/herself that his beliefs are not that contradictory or that the way he acted was not against his beliefs.
In this example, Professor Stewart wrote a very positive letter of recommendation for a student despite having doubts about her competence. Now, he is developing more favorable attitudes about the student's abilities. We can see that he acted in a way that was contrary to his beliefs (he wrote a positive letter when he had doubts) so he is now trying to reduce the stress this generates convincing himself that the student has more abilities and looking at her in a more favorable light. Thus, this would be an example of the Cognitive Dissonance Theory.