How does princess Belle win the trust of the beast??

Though Beauty is supposed to be a prisoner, it is the Beast who is imprisoned. In spite of the fact that he doesn’t want her to leave him, he agrees that Beauty should go home and visit her inconsolable father. That short-lasting separation helps Beauty to understand that she has already fallen in love with the Beast. She doesn’t need either the castle or the treasures that are kept there. She values love and friendship of the Beast more than anything else in the whole world.