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Gaurav Seth 6 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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Amit Kumar 6 years, 1 month ago
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