I don’t believe you can separate them.
Wait—I’m wrong. That was a gut response, but on further examination I don’t think it’s true. If you have ever had a child (or other beloved person) go through a phase where he is sneaking around, stealing from your purse, lying to you, etc., you have known what it is to love someone you can’t trust. The same if you have ever had an unfaithful partner.
Likewise, now that I think about it, if you have put yourself in the hands of a doctor or followed a competent leader, you have probably trusted someone whom you wouldn’t say you loved.
So yes, you can separate them.
Now, then, @AmWiser: are you asking if I would rather love someone or trust the person, or are you asking if I would rather BE loved or BE trusted?