Question

If sinA=4/5, then 1+cosA/2TanA=

Answer 1

Question :- If sinA = (4/5), then find (1+cosA)/(2TanA) = ?

Solution :-

we know That :-

sin theta = Perpendicular/Hypotenuse

cos theta = Base/Hypotenuse

tan theta = Perpendicular/Base

cosec theta = Hypotenuse/Perpendicular

sec theta = Hypotenuse/Base

cot theta = Base/Perpendicular

So,

=> sinA = (4/5) = Perpendicular/Hypotenuse

we get :-

=> Perpendicular = P = 4

=> H = 5

By Pythagoras Theoram ,

=> B = √(5)² - (4)²

=> B = √(25 - 16)

=> B = √9

=> B = 3 .

So,

=> cosA = Base/Hypotenuse = 3/5

=> tanA = Perpendicular/Base = 4/3

Putting both Values we get,

=> (1+cosA)/(2TanA)

=> ( 1 + 3/5) / ( 2 * 4/3)

=> (8/5) / (8/3)

=> (8/5) * (3/8)

=> (3/5) (Answer).