if anakin can believe a dude who literally just confessed to lying to absolutely everyone about absolutely everything for ten consecutive years when they tell him he can save his wife by killing a hundred toddlers, then anakin can and will believe literally anything you tell him. absolutely any storm trooper could tell darth vader that he just got fired and he would instantly start sobbing

As an addition! Anakin can also believe stuff nobody tells him and nobody suspects without any evidense! As an example: Anakin believing that Padme had conspired behind his back for Obi-Wan to kill him.