An Etymological Dictionary of the German Language/trauen
trauen, vb., ‘to trust, confide; marry,’ from MidHG. trûwen, wk. vb., ‘to hope, believe, trust’ (also ‘to betroth, unite in marriage’), OHG. trûên (trûwên), ‘to believe, trust.’ Comp. Goth. trauan, wk. vb., ‘to trust, confide,’ OSax. trûôn, Du. vertrouwen, ‘to trust, confide’ (but trouwen, ‘to marry’). A derivative of the Teut. root trū̆, treu, ‘to have confidence,’ mentioned under traut and treu.