Find the value of `(1-sin^(2)A)(1+tan^(2)A)`.

Answer

To find the value of \( (1 - \sin^2 A)(1 + \tan^2 A) \), we can use some trigonometric identities. Let's solve it step by step.

### Step 1: Use the Pythagorean Identity
We know from the Pythagorean identity that:
\[ 1 - \sin^2 A = \cos^2 A \]
So we can rewrite the expression:
\[ (1 - \sin^2 A)(1 + \tan^2 A) = \cos^2 A (1 + \tan^2 A) \]

### Step 2: Use the Identity for Tangent
We also know that:
\[ \tan^2 A = \frac{\sin^2 A}{\cos^2 A} \]
Thus, we can express \(1 + \tan^2 A\) as:
\[ 1 + \tan^2 A = 1 + \frac{\sin^2 A}{\cos^2 A} = \frac{\cos^2 A + \sin^2 A}{\cos^2 A} \]
Using the Pythagorean identity again, \( \cos^2 A + \sin^2 A = 1 \):
\[ 1 + \tan^2 A = \frac{1}{\cos^2 A} \]

### Step 3: Substitute Back into the Expression
Now substituting this back into our expression:
\[ \cos^2 A (1 + \tan^2 A) = \cos^2 A \cdot \frac{1}{\cos^2 A} \]

### Step 4: Simplify the Expression
Now we can simplify:
\[ \cos^2 A \cdot \frac{1}{\cos^2 A} = 1 \]

### Final Answer
Thus, the value of \( (1 - \sin^2 A)(1 + \tan^2 A) \) is:
\[ \boxed{1} \]