Last Friday, we had a person interviewing for a math teaching job at my school do a demo lesson in one of my precalculus classes. His lesson was on deriving cos(a-b)=cos(a)cos(b)+sin(a)sin(b). I was a little bummed because I like to teach that lesson. He taught it using a proof that our textbook uses.
Today, to keep the two classes in sync with each other in terms of content, I also did this lesson. I did it essentially the same way the interviewing teacher did it, except without giving the students much information. In essence, I gave them these two questions, which led them to the formula.
They did quite well on this. I had to do a little hand holding at times for various groups, but I was happy that overall they were able to get from point A to point B quite well. (Before we did it, I was slightly nervous that it was a bit too open ended.)