I know a social worker who uses bitachon to help her patients who are dealing with anxiety. I imagine this is very common amongst Frum therapists. I think it works something along the lines of what Yitzymotcha described.
And I agree with you, Yitzy, you should never tell someone to have bitachon. That is one of the stupidest things you can say to someone who is expressing concern about something. Someone just did that to me recently, and I think it had the effect of making me more nervous.
If someone understands what bitachon is, they would realize that telling someone to have bitachon can’t possibly help them to have bitachon. It is an internal process that can only come from the person himself and can’t be imposed from the outside.