Having to trust someone is not easy, but to have someone to trust you is harder. And it goes like that every where in life.
Let's pick an example from a first person shooting game (CS, BF, COD, you name it).
If you would trust your partner that he'd cover your back, you won't even think of looking back. Same goes to your partner. He trusts that you will cover his back too. Here we see a mutual understanding, even it won't be beneficial at all times. AND even if you died of backstabbing (attack from behind), you wouldn't blame your friend as you trust that he did his best protecting your ass. After all, you'll be respawn back in no time. It is just a game.
What if it is not a game?
Now that's the real question. What if you are a SWAT (Special Weapons and Tactics) team and the success of your mission depends entirely on your team working? Enemies attack from all direction and you need to trust that each of your team members will cover for you, as they expect the same from you. One slight of mistrust and you turned to check your own back, you might just jeopardize the mission and the lives of your entire team. It's life here we are talking about. REAL LIFE. No respawn.
What I'm trying to say here is that (which is pretty obvious if you asked me) trust basically holds the world together.
If someone trusts you, don't lose it. Don't take "I trust you" lightly. It might not be as affectionately as "I love you" but it certainly sounds better than "I hate you and I don't want to see you for the rest of my lives and the next because you cheated on me and I'm so dumb believing you."
Trust is important too in friendship or in relationship. Though I think it serves a much greater purpose in relationship as both sides are expected to spend the rest of their lives together (so the "I hate you and I don't want to..." above will really affect your relationship very much).
Oh and another thing, when someone trusts you, you should never doubt them even for a moment. They have offered you something that is priceless and in what position you think you are to doubt them?
The thing with trust is that you must always remain considerate. It is a hard thing to do, being considerate, but it sure does a great job in making people feel good about it. In fact, it made them felt SO good, they did not realised you are being considerate. But again, since you are a considerate being you won't mind people ignoring your considerateness. If everyone adapt to being considerate, the world would totally be a better place to live in.
I shall end this post with a simple quote.
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