What are some of the ways that teens will try to hide that they are anorexic?

Infinite. Teens are masters of deception and cover up. Excuses will abound for whatever their parents observe. Usually a sibling or close friend will "rat them out." if your teen has self image problems, spends too much time at the gym, obsesses over foods and recipes, appears too thin, then you should be suspicious.
Strongly agree. There are even websites that specialize in teaching anorexics how to fool family members and professionals about the extent of their weight loss--and that assert that anorexia is not a "disorder" but a lifestyle choice.