Find tan2A when tanA = 1/3 and π<A<3π/2.
A) 4/5
B) 5/4
C) 3/4
D) 3/5
So A in in quadrant III
tan 2A = 2tanA/(1 - tan^2 A)
= 2(1/3)/(1 - 1/9)
= (2/3) / (8/9)
= (2/3)(9/8)
= 18/24 = 3/4
To find tan(2A), we can use the double-angle formula for tangent:
tan(2A) = (2tanA)/(1 - tan^2A)
Given that tanA = 1/3, we can substitute this value into the formula:
tan(2A) = (2*(1/3))/(1 - (1/3)^2)
Simplifying, we have:
tan(2A) = (2/3)/(1 - 1/9)
tan(2A) = (2/3)/(8/9)
To divide by a fraction, we can multiply by its reciprocal. Therefore:
tan(2A) = (2/3)*(9/8)
tan(2A) = 18/24
Reducing to its simplest form, we have:
tan(2A) = 3/4
Therefore, the answer is C) 3/4.