Why do historians need archaeologists and and anthropologists to study prehistory?

Answer 1

The answer is in the term "prehistory". There is no history from that time, so we need other scientist to figure out what was going on and who or what was there.
Historians rely on facts about history often well known ones. They may wish to cover new ground by using their insight to interpret information a different way. With that said, many historical events, undiscovered new ancient cities, weather situations, can allow historians to have additional information then earlier. Archaeologists & anthropologists are making new discoveries each day in some part of the world. Historians cannot "study" from their libraries. They can access the information uncovered by the aforementioned scientists. A classic example is the Dead Sea Scrolls which in some minds presented new & better information about what is usually called the Old Testament.

Another example might be found in the Caribbean Sea. Historians have written about the Spanish "gold" galleons that brought precious metals from the New World back to Spain. Should a massive amount of new shipwrecks be found in the Caribbean, then estimates of how many such ships Spain had in the 16th Century may change.

There has been much study of the Native Americans in North & South America. For the most part, certain ideas about the Native Tribes in the North,are limited by the lack of written languages. A "dig" by an archaeologists could possibly uncover a "lost Native language". This new information would change certain views held by historians who study the events & peoples of the New World.

The above examples hold true not only for ancient history but also of different eras of human history such as ancient Native American Tribes.