Want people to trust you, well then trust them. It takes time to see if somebody is worth trusting. You get a certain type of person that nobody will ever trust and they will never trust anyone either, give them a chance and trust them with something small. It might mean something big to them and that will make them want to trust you.
That being said, some people will never like you even if is for no good reason, the same goes for trust, some people just don't trust us for no good reason.
Stick to what you say and remember what people say, people tend to trust people
that take note of the things they say.