A funny thing happens when you show someone you trust them: they begin to let their guard down. If you want someone to trust you more, do your best to show them how much trust you have in them.
Photo by California National Guard.
People are more inclined to trust someone that appears to be on the same team. As author Heidi Grant Halvorson explains in her book No One Understands You and What To Do About It, a great deal of trust can come from simple reciprocity:
We are more likely to feel we can trust someone who has trust us first -- someone who has been openly cooperative rather than competitive and put others' interest above their own... Far from seeing you negatively, the perceiver is likely to feel that this invitation to intimacy indicates that you are on the same team.
What are the best ways to show that you trust someone? Always give them freedom to make their own decisions and learn from their mistakes (being a backseat driver shows very little trust, for example), share appropriate personal information with them, and affirm some of their views. If they say that they can handle a task or achieve a goal, a simple "I know you can" will go a long way. The more you can outwardly express your trust in them, the more they will begin to find trust in you.