(1 + tan θ)² + (1 - tan θ)² is equal to :

1. 2 cosec² θ

2. 2 sec² θ

3. cosec² θ

4. sec² θ

Solving,

⇒ (1 + tan θ)² + (1 - tan θ)²

⇒ 1 + tan² θ + 2 tan θ + 1 + tan² θ - 2 tan θ

⇒ 2 + 2 tan² θ

⇒ 2(1 + tan² θ)

Substituting, 1 + tan² θ = sec² θ, we get :

⇒ 2 sec² θ.

Hence, Option 2 is the correct option.