To find the maximum (Amax) and minimum (Amin) values of A = 2 + 3sin^2(X), we need to know that the maximum value that the function sin^2(X) can reach is 1 (sin^2(X) ≤ 1 for all values of X).
When sin^2(X) reaches its maximum value of 1, then A will have its maximum value when 3 * 1 + 2 = 5, and its minimum value when sin^2(X) reaches its minimum value of 0, in which case A = 2.
Therefore, Amax = 5 and Amin = 2.