Are only True Beliefs Effective?

I’m interested in the relationship between truth and effectiveness of a belief (or a theory).

Are true beliefs the only ones to be useful, solve problems, achieve goals?

Is there a correspondence between what is true and what is effective?

Positivism says yes (look at the relationship of correspondence between science and technology, its application).

I also say yes: historically it seems true, humankind is ever more effective and has ever more power as scientific knowledge of reality progresses.

Whenever this is not the case, it is because one acts “as if”. That is, it happens if a false belief makes one behave in the same way as a true one.

A good example is: to suffer for the death of a loved one does not serve any purpose. But if somebody simply says that to him/herself, it may have no effect.

If, on the other hand, one thinks: “I’ll see that person again in Heaven”, s/he behaves as one who says: “Suffering serves no purpose”, even though s/he does that by following a, let’s assume, false belief, which in this case leads to the same behaviour that would be inspired by a true belief.

I've assumed, for the sake of argument, that this belief is false, but in reality it would be more accurate to say that it's not certain.