Final answer:
To evaluate csc2A, we need to find the value of secA first. Using the Pythagorean identity cos^2A = 1 - sin^2A, we can find the value of cosA. Then, using the fact that secA = 1/cosA, we find secA. Finally, csc2A is equal to (1/sinA)^2.
Step-by-step explanation:
To evaluate csc2A, we need to find the value of secA first. Since sinA = 4/5, we can use the Pythagorean identity cos^2A = 1 - sin^2A to find cosA. Plugging in the value of sinA, we get cosA = √(1 - (4/5)^2) = 3/5.
Using the fact that secA = 1/cosA, we find secA = 5/3.
Finally, csc2A = (1/sinA)^2 = (1/(4/5))^2 = (5/4)^2 = 25/16.