What were the intended purposes of the monroe doctrine and the roosevelt corollary? ?

First off, the Monroe Doctrine, was actually basically a statement. It stated that if Europe, tried to colonize land around North America the US would see it as an act of aggression and respond in kind. (AKA Europe can't stick their nose around the US or else it'd  be considered an act of "war".) The Roosevelt Corollary was just a big stick-on to the Monroe Doctrine. It stated that the US could intervene in Latin American affairs whenever they deemed it necessary to.(Also, whenever they need to maintain political and economic activities, could the US interfere.)