I've often heard "believe in each other" used, but considering that "believe" is a transitive verb, it would seem to be grammatically correct to say "We have to believe each other", instead of saying "We have to believe in each other." Is this wording grammatically correct? Or is it not acceptable enough to use?

If it is grammatically correct, do both sentences convey the same meaning?

I'd appreciate it if you could help me understand the usage.