Mr. Wilhelm-
I was unable to comment in the comment box, so I have posted my response:

I find simplifying and solving multiple-angle equations to be challenging. For example, knowing where to start and how to continue on when solving equations such as cos5x-7cos2x=8 is difficult as these problems may become very long, and many times lead to dead ends. In addition, several different identities must be substituted in for other terms in order to solve these problems. There are often several identities to choice from, and some identities may equal more than one thing, as does cos2x. Deciding which identity to substitute in is often difficult.

Daynna Myers