How do sociologists examine the social world using both history and biography? In relation to this subject matter, what is macrosociology? What is microsociology?

Sociology as whole is the scientific and systematic study of human groups, based on society, culture, and relationships.

Macrosociology isjust an broad approach to sociology which emphasizes the analysis of social systems and populations on a large scale, at the level of social structure, and often at a necessarily high level of theoretical abstraction. while Microsociology is one of the main levels of analysis (or focuses) of sociology, concerning the nature of everyday human social interactions and agency on a small scale: face to face.

and the distincts difference between them is that one of the main branches of this science, macrosociology, involves the study of society as a whole, while another, microsociology, involves the study of individual human interactions

Explanation:

so taking about the examine the social World using both history and biography has to do with the fact that "history as it is " is the fact that society is located in a broad stream of events, while "biography" refers to an individual's specific experiences in life time.