If 90o<A<180o and sinA=4/5, then tanA2 is equal to
First, we can use the given information to find the value of cosA.
Since we know that sinA = 4/5, we can use the Pythagorean identity sin^2(A) + cos^2(A) = 1 to find cosA.
sin^2(A) + cos^2(A) = 1
(4/5)^2 + cos^2(A) = 1
16/25 + cos^2(A) = 1
cos^2(A) = 9/25
cosA = √(9/25) = 3/5
Now, we can use the identity tan^2(A) + 1 = sec^2(A) to find tan^2(A).
tan^2(A) + 1 = sec^2(A)
tan^2(A) = sec^2(A) - 1
Since secA = 1/cosA, we can substitute this into the equation.
tan^2(A) = (1/cosA)^2 - 1
tan^2(A) = (1/(3/5))^2 - 1
tan^2(A) = (5/3)^2 - 1
tan^2(A) = 25/9 - 1
tan^2(A) = 16/9
Therefore, tan^2(A) = 16/9.