It's not clear to me how you prove that you did the work for the course. As far as I can tell with Coursera, all it takes is for you to input the correct answers in order to pass (i.e. you may have found the answers online, had a friend help you etc). Identity is still unsolved.
Coursera often changes the numbers/units for math problems and switch up problems on every attempt. You can cheat at a 4-year physical college, but it's harder. If you are trying to cheat on courses, you probably shouldn't be in college :)