Question

If 2sec²θ + tan²θ = 17 then find the value of cotθ. 
1. √5
2. (1/√5)
3. √3
4. (1/√3)

Answer 1

Correct Answer - Option 2 : (1/√5)

Given

2sec2θ + tan2θ = 17 

Concept

Sec²θ - tan²θ = 1

Sec²θ = 1 + tan²θ 

Cotθ = (1/tanθ)

Calculation

 We have 2sec2θ + tan2θ = 17

⇒ 2(1 + tan²θ ) + tan²θ = 17

⇒ 2 + 2tan²θ + tan²θ = 17

⇒ 3tan²θ = 15

⇒ tan²θ = (15/3)

⇒ tan²θ = 5 

⇒ tanθ = √5 

⇒ cotθ = (1/√5)

∴ Cotθ = (1/√5)