$\dfrac{\sin^4 A − \cos^4 A}{1 − \sin^2 A}$ is equal to :

1. cot² A − 1

2. tan² A − 1

3. 1 − cot² A

4. 1 − tan² A

$\Rightarrow \dfrac{\sin^4 A − \cos^4 A}{1 − \sin^2 A} \\[1em] \Rightarrow \dfrac{(\sin^2 A − \cos^2 A)(\sin^2 A + \cos^2 A)}{\cos^2 A} \\[1em] \Rightarrow \dfrac{\sin^2 A − \cos^2 A}{\cos^2 A} \\[1em] \Rightarrow \dfrac{\sin^2 A }{\cos^2 A} - 1 \\[1em] \Rightarrow \tan^2 A - 1 .$

Hence, option 2 is the correct option.