The purpose of placing the line "it's politics of believing in things unseen; of believing in what this country might be; and of standing up for that belief and fighting for it when it's hard," at the end of his speech is to

Adding that line at the end of a speech is an appeal to Pathos.

Explanation:

Pathos is a feature of rhetoric related to appealing to the emotional side of an audience that is listening to the speech. Pathos has the function of seeking public empathy for a cause and, therefore, uses words that generate a strong feeling in people about something.

In the line "it's politics of believing in things unseen; of believing in what this country might be; and of standing up for that belief and fighting for it when it's hard," we can see that the author of the speech is appealing to the patriotic feeling of people, causing the audience to be moved, about the need to fight for the country, even if it is difficult to obtain victory. For this reason, we can say that the author made an appeal to pathos, when he added this line to the speech.