Prove the following identities :

$\dfrac{\text{cos θ cot θ}}{\text{1 + sin θ}}$ = cosec θ - 1

(1 + cot² A) + (1 + tan² A) is equal to :

1. $\dfrac{1}{\text{sin}^2 A - \text{cos}^2 A}$

2. sec² A - cosec² A

3. sin² A - sin⁴ A

4. sec² A.cosec² A

$\dfrac{1}{\text{cot θ + tan θ}}$ is equal to :

1. sin θ + cos θ

2. sin θ. cos θ

3. $\dfrac{1}{\text{sin θ. cos θ}}$

4. $\dfrac{1}{\text{sin θ + cos θ}}$

(sec θ - cos θ)² - (sec θ + cos θ)² is equal to :

1. 4

2. 2

3. -2

4. -4