NEW YORK, Aug 10 (Reuters) - Faced with mounting legal pressures and demands for his departure from President Joe Biden and others, New York Governor Andrew Cuomo resigned on Tuesday following an inquiry that found he sexually harassed 11 women, capping a startling downfall for one of the most prominent politicians in the United States. A Democrat who had served since 2011 as governor of the fourth most-populous state, Cuomo made the announcement a week after New York Attorney General Letitia James released the results of a five-month independent investigation that concluded he had engaged in conduct that violated U.S.