Here is Michael Stuben's effort to introduce the trigonometry sum and difference formulas in an interesting way:
As we all know, some of the people to whom we are attracted are not attracted to us. And it is not unusual for a person who has shown interest in us to later lose interest in us. Maybe that is a good thing, because it forces us to date a lot of people and to become more experienced in maintaining relationships.
Anyway, this is the story of Sinbad and Cosette. Sinbad loved Cosette, but Cosette did not feel the same way about Sinbad. Naturally, when Sinbad was in charge of their double date, he put himself with Cosette, and he put his brother with her sister:
sin(A + B) = sin A cosB + cosA sinB.
sin(A - B) = sin A cosB - cosA sinB.
Sinbad loved to tell people that his and Cosette's signs were the same.
However, when Cosette was in charge of the double date she placed herself with her sister and put Sinbad with his brother. She made sure everyone knew that their signs were NOT the same:
cos(A + B) = cosA cosB - sinA sinB.
cos(A - B) = cosA cosB + sinA sinB.
Also, notice that Cosette placed herself and her sister BEFORE Sinbad and his brother. This detail was important to Cosette. She was very snobby, you know.