Introduction:
In this question, we are given the values of sin^2A, cos^2B, cos^2A, cos^2B, sin^2A, and sin^2B. We need to determine the value of each expression and explain the steps involved in the calculations.

Solution:
To evaluate the given expressions, we will use the trigonometric identities:

- sin^2A + cos^2A = 1
- sin^2B + cos^2B = 1

Step 1: Evaluating sin^2A:
We are given the value of sin^2A. We can rewrite it as sin^2A + cos^2A = 1. Since sin^2A is already given, we can substitute the value in the equation to find the value of cos^2A.

Step 2: Evaluating cos^2B:
Similarly, we are given the value of cos^2B. We can rewrite it as sin^2B + cos^2B = 1. Substituting the given value of cos^2B in the equation, we can find the value of sin^2B.

Step 3: Evaluating cos^2A cos^2B:
We know the values of cos^2A and cos^2B. To find the value of cos^2A cos^2B, we can multiply the given values.

Step 4: Evaluating sin^2A sin^2B:
Similarly, we know the values of sin^2A and sin^2B. To find the value of sin^2A sin^2B, we can multiply the given values.

Summary:
- sin^2A + cos^2A = 1, where sin^2A is given.
- sin^2B + cos^2B = 1, where cos^2B is given.
- Substitute the given values to find the values of cos^2A and sin^2B.
- Multiply the values of cos^2A and cos^2B to find cos^2A cos^2B.
- Multiply the values of sin^2A and sin^2B to find sin^2A sin^2B.

Answer:
The values of the given expressions are:
- sin^2A = given value of sin^2A
- cos^2B = given value of cos^2B
- cos^2A cos^2B = product of the given values of cos^2A and cos^2B
- sin^2A sin^2B = product of the given values of sin^2A and sin^2B.