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Answers
Given : CosA = 4/5
To Find : Value of TanA
3/5
3/4
4/3
5/3
Solution:
CosA = 4/5
Cos = Base / Hypotenuse
Base = 4k and Hypotenuse = 5k
Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
=> (perpendicular) = √(5k)² -(4k)² = 3k
Tan = Perpendicular /Base
=> Tan A = 3k/4k
=> Tan A = 3/4
Another method :
CosA = 4/5
Cos²A + Sin²A = 1
=> SinA = 3/5
TanA = SinA/CosA = 3/4
or
SecA = 1/CosA = 5/4
sec²A = 1 + tan²A
=> (5/4)² = 1 + Tan²A
=> (3/4)² = Tan²A
=> 3/4 = TanA
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