You never will know. You can, believe, disbelieve or leave them.

I really agree with kevin. There is no method to examine if she/he is sincere to you. What you can do is just trying your best to believe him/her if you love him/her enough. Good relationship lies in trust...Don't try to test if he/she is sincere, that will break your relationship. i have similar experience good luck!

S/he remembers little details to prove that s/he listens to what you have to say :)

We can understand it by their actions.