$\text{cot}^2 \text{ θ} - \dfrac{1}{\text{sin}^2 \text{ θ}}$ is equal to

1. 1

2. -1

3. sin² θ

4. sec² θ

Given,

$\text{cot}^2 \text{ θ} - \dfrac{1}{\text{sin}^2 \text{ θ}}$

The equation can be written as,

$\Rightarrow \dfrac{\text{cos}^2 \text{ θ}}{\text{sin}^2 \text{ θ}} - \dfrac{1}{\text{sin}^2 \text{ θ}} \\[1em] \Rightarrow \dfrac{\text{cos}^2 \text{ θ} - 1}{\text{sin}^2 \text{ θ}} \\[1em] \Rightarrow \dfrac{-(1 - \text{cos}^2 \text{ θ})}{\text{sin}^2 \text{ θ}} \\[1em] \Rightarrow \dfrac{-\text{sin}^2 \text{ θ}}{\text{sin}^2 \text{ θ}} \\[1em] \Rightarrow -1.$

Hence, Option 2 is the correct option.