If 90o<A<180o and sinA=4/5, then tanA2 is equal to

Answer 1

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.