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History | Prehistory |
The study of time period succeeding prehistory is called history | The study of the time period preceding history is called prehistory. |
History is the study of the past starting from the time period when the writing system was introduced and written records were maintained. | Prehistory is the study of the past, even before writing was invented and written records were maintained. It is the study of the time period between the usage of stone tools and the invention of the writing system. |
Written records of the past events are the source of information. | Artifacts, Carvings on rocks etc are the sources of information while studying prehistory. |
Research on History is carried out by historians. Rare manuscripts written on leaves, dried animals skins, and papers are some of the sources used to study history. | Research on prehistory is carried out by archaeologists and anthropologists who use excavation, geology, molecular genetics, palaeontology etc. Hence a wide variety of social and natural sciences are used to study prehistory. |
Study of History can be classified into different domains like Ancient History, Contemporary History, Modern History, Political History, Military History, Cultural History, Economic History, Environmental History, History based on different Geographical locations, People’s history, Intellectual history etc. | Prehistory studies 3 different time periods – stone age, bronze age and iron age. |
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Gaurav Seth 5 years, 2 months ago
Given:
tan x = 1/7
tan y = 1/3
To Prove: cos 2x = sin 4y
We know that
tan x = opposite / adjacent = 1/7
So using these value in right angle triangle ABC and Pythagoras theorem,
AC² = 1² + 7² = 1 + 49 = 50
AC = √50 = 5√2
⇒ sin x = opposite/hypotenuse = 1/5√2
⇒ cos x = adjacent/hypotenuse = 7/5√2
Also,
tan y = opposite / adjacent = 1/3
So using these value in right angle triangle LMN and Pythagoras theorem,
AC² = 1² + 3² = 1 + 9 = 10
AC = √10
⇒ sin y = opposite/hypotenuse = 1/√10
⇒ cos y = adjacent/hypotenuse = 3/√10
Now,
LHS = cos 2x = 2cos² x -1 = 2(7/5√2)² - 1 = 2(49/50) - 1
= 24/25
RHS = sin 4y = 2 sin 2y cos 2y
= 4 sin y cos y (2cos² y -1)
= 4 (1/√10)(3/√10) ( 2(3/√10)² - 1 )
= (12/10) ( 9/5 - 1 )
= (6/5) ( 4/5 )
= 24/25
LHS = RHS
Hence proved.
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Cell was discovered by an English Botanist, Robert Hooke in 1665. He used self-designed microscope to observe cells in a cork slice back then.
Cells are called the structural and functional unit of life because all the living organisms are made up of cells and all the functions that take place inside the organisms are performed by cells.
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