공부하고

In a sentence

• 나는 도서관에서 공부하고 있어요.

  I am studying in the library.

  Here, '공부하고' is part of the present progressive verb phrase '공부하고 있어요', indicating an ongoing action, which is 'studying'.

• 나는 수학을 공부하고 친구는 영어를 공부해요.

  I study math, and my friend studies English.

  In this sentence, '공부하고' connects two phrases where the speaker describes their study activity and contrasts it with their friend's activity.

• 공부하고 나서 운동을 할 거예요.

  I will exercise after studying.

  The usage of '공부하고' here indicates a sequential action, meaning that studying is completed before the next action, exercising.