Question

(1 + tan θ)² + (1 − tan θ)² is equal to ______.

विकल्प

• 2 coseс² θ

• 2 sec² θ

• coseс² θ

• sec² θ

Answer 1

(1 + tan θ)² + (1 − tan θ)² is equal to 2 sec² θ.

Explanation:

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.