this seems to be a machlokes.
While the chazon ish in emunah and bitachon takes side 2.
the madregas haadam takes side one.
The vilna gaon on mishle “??? ??” ??? ??? ??? ???? ?? ????
brings the gemara which tries to understand why the pasuk
???? ?? ?” ???? ???? ??????
uses the word ???? and not ????
the gemara clarifies from a story of rabbah(?) who had a heavy burden and along came a merchant with a camel and told him to place his ???? on the camel, from here the gemarah understands the word.
The Vilna Gaon said, chazal did not need the this story to teach them the word, rather they were not sure if bitachon was enough to garner results or you needed hishtadlus, when Rabba(?) who had strong bitachon, did not action and his needs were taken care of, even when usually you would need to pay for this kind of service and search out for someone to help. The chazal learn from here that ???? implies, that by bitachon alone all your needs will be taken care of.
Another gemara, where a poor person comes to rabba, asking for chicken and aged wine, and rabbah replies, “how can you ask for such fancy stuff when you are taking from tzedaka?”
The pauper replies, “i am not taking from you, rather i am taking from hashem”
when in walks rabbas sister who he has not seen for 13 years, with a gift of plenty of chicken and old wine.
From here rabba understands that by trust alone your needs will be taken care of.
The ramban seems to imply that by trust alone one can be healed from sickness, and the pasuk, verapo yerape, is giving permission to those who lack bitachon to go to a doctor.