Question

2
il) Prove that sec^2theta+ cos^2theta
can never be less than 2.
​

Answer 1

Given,

sec²θ + cos²θ

We know,

• sec²θ = 1 + tan²θ
• cos²θ = 1 + cot²θ

⇒ sec²θ + cos²θ  = 1 + tan²θ + 1 + cot²θ

⇒ sec²θ + cos²θ = 2 + tan²θ + cot²θ

From this we can understand that

sec²θ + cos²θ > 2

Hence Proved !!!