Can i get tax deductions if i don't have a business license?

I am starting a Personal Training Business which will be based out of my home office, i already spoke with the licensing department with the City of Phoenix and they said i do not need a business license because i am supplying a service and not selling something. I am going to get an LLC but i am wondering will i still be able to write things off for the business with just an LLC and no business license?