If sec2 θ + tan2 θ = 3 then find the value of cot θ.

1.	If sec2 θ + tan2 θ = 3 then find the value of cot θ.
Answer» Correct Answer - Option 2 : 1 Concept: 1 + tan2 θ = sec2 θ sec2 θ - 1 = tan2 θ Calculation: Given: sec2 θ + tan2 θ = 3 To Find: Value of sec θ sec2 θ + tan2 θ = 3 Subtracting 1 both sides, we get ⇒ sec2 θ + tan2 θ - 1 = 3 - 1 ⇒ tan2 θ + tan2 θ = 2 (∵ sec2 θ - 1 = tan2 θ) ⇒ 2tan2 θ = 2 ⇒ tan2 θ = 1 ∴ tan θ = 1 Now, cot θ = \(\rm \frac {1}{\tan \theta} = \frac 1 1 = 1\)

Answer» Correct Answer - Option 2 : 1

Concept:

1 + tan2 θ = sec2 θ

sec2 θ - 1 = tan2 θ

Calculation:

Given: sec2 θ + tan2 θ = 3

To Find: Value of sec θ

sec2 θ + tan2 θ = 3

Subtracting 1 both sides, we get

⇒ sec2 θ + tan2 θ - 1 = 3 - 1

⇒ tan2 θ + tan2 θ = 2 (∵ sec2 θ - 1 = tan2 θ)

⇒ 2tan2 θ = 2

⇒ tan2 θ = 1

∴ tan θ = 1

Now,

cot θ = \(\rm \frac {1}{\tan \theta} = \frac 1 1 = 1\)

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