(一).You can trust me. 相信我吧。/你可以信任我。
This is a way to say "I am honest." The speaker wants someone to believe he is a good man.
Trust me.相信我。

原音重现：

A: I am not sure if I want to buy this.
我不知道该不该买这个。
B: You can trust me. I won't cheat you.
相信我，我不会骗你的。

美剧表达：
I'm your friend, so you can trust me.我是 你的朋友，你可以信任我。

Don't worry, all right? You can trust me.不要担心，好吗？相信我。

You can trust me, Allen. I'm not going to hurt you.相信我，艾伦，我不会伤害你的。

(二).Rest assured.放心吧。/不要担心。

This usually means “Believe me.” It is a way to tell someone that something can be trusted.

原音重现：

A: How can I trust that you will repair my car correctly?
我怎么相信你能把我的车修好？
B: Rest assured that I will fix it so it works well.
放心吧，我一定会把它修好的。

美剧表达：
Rest assured. Everyone's secrets are safe.放心吧，所有人的秘密都不会泄。

Rest assured, and we have not forgotten.放心吧，我们没有忘记。