So what is the best way to deal with a cougar?
If attacked, same as a black bear. Fight back. It is possible to bluff them by holding your arms above your head and make yourself as big as possible. Don't corner them, don't run away. From all accounts that I've read, they die pretty quickly when shot, as others have pointed out, the problem is knowing that they are coming for you...
Tigers attack from the rear also, and one trick that I learned from watching nature shows, is wearing a hat with a neck covering, and painting a mean face on it. The theory is that the cougar (or tiger) sees the face, and doesn't know that it's your back. It's worth a try!