If y = sec² θ + cos² θ, where \(0<\theta < \dfrac{\pi}{2}\), then which one of the following is correct?

Question

Question

Answer 1

Concept:

Trigonometric Property :

\(\sec \;\theta = \dfrac {1}{\cos\;\theta}\)

Calculations:

Given, y = sec2 θ + cos2 θ, where

⇒ y = sec2 θ + cos2 θ - 2 + 2

⇒ y = sec2 θ - 2 sec θ cos θ + cos2 θ + 2

⇒ y = (sec - cos θ)² + 2

As (sec - cos θ)2 \(\geq\) 0

⇒ (sec - cos θ)2 + 2 \(\geq \) 2

⇒ y ≥ 2

Hence, if y = sec2 θ + cos2 θ, where \(0<\theta < \dfrac{\pi}{2}\), then y ≥ 2