1.

If 2sec2θ + tan2θ = 17 then find the value of cotθ. 1. √52. (1/√5)3. √34. (1/√3)

Answer» 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)



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