1. The problem asks to find the expression equivalent to $1 + \tan^2(A)$. 2. We use the Pythagorean identity in trigonometry: $$1 + \tan^2(A) = \sec^2(A)$$ 3. This identity comes from the fundamental Pythagorean identity: $$\sin^2(A) + \cos^2(A) = 1$$ Dividing both sides by $\cos^2(A)$ gives: $$\frac{\sin^2(A)}{\cos^2(A)} + \frac{\cos^2(A)}{\cos^2(A)} = \frac{1}{\cos^2(A)}$$ Simplifying: $$\tan^2(A) + 1 = \sec^2(A)$$ 4. Therefore, the correct answer is $\sec^2(A)$.