$\dfrac{1 + \text{tan}^2 A}{1 + \text{cot}^2 A}$ is equal to

1. sec² A

2. -1

3. cot² A

4. tan² A

Given, $\dfrac{1 + \text{tan}^2 A}{1 + \text{cot}^2 A}$.

By using trigonometric identities the above equation can be written as,

$\Rightarrow \dfrac{\text{sec}^2 A}{\text{cosec}^2 A} \\[1em] \Rightarrow \dfrac{\dfrac{1}{\text{cos}^2 A}}{\dfrac{1}{\text{sin}^2 A}} \\[1em] \Rightarrow \dfrac{\text{sin}^2 A}{\text{cos}^2 A} \\[1em] \Rightarrow \text{tan}^2 A$

Hence, Option 4 is the correct option.