One of the facets of trust, which is particularly important to teens, is respecting their privacy. Your teen may not tell you as much as you'd like about what she's doing after school or who she's hanging out with, but prying into her business should only be a last resort. Sneaking into your son's room while he's out or asking your other children to report to you behind her back cannot replace real conversations with your teen (no matter how hard that might be), and broken trust is almost impossible to regain.
Your teen needs to know that you will do as you say. If you've promised to come to your son's jazz recital but don't show, you risk losing his trust; he may think you don't care. Equally, if you've told your daughter that she can't go to a party until she finishes her chores but you let her go anyway, she has a reason to try manipulating you in the future.
If you had good reasons for your decision to change your plans or your mind, you should explain. In this way, you can mend broken trust, and at the same time, model for your children the behaviors you expect of them: open and honest discussion of what's going on, and apologies for setting false expectations.
Trust must be earned; you can't force your teen to trust you. Be available to your teens when they are prepared to talk to you and take them seriously. Let them in on some of your own dilemmas as a sign of your trust in them. Trust is a two-way street -- you have to give some to get some. If there are situations in which you don't trust your teens, let them know why and allow them to do the same for you.