Question

If 0 ≤ θ ≤ π/2 and sec²θ + tan²θ = 3 then θ is :
1. π/6 radian
2. π/4 radian
3. π/3 radian
4. 5π/12 radian

Answer 1

Correct Answer - Option 2 : π/4 radian

As per the question

sec2θ + tan2θ = 3

∵ sec2θ = 1+ tan2θ

⇒ 1 + tan2θ + tan2θ = 3

⇒ 2tan2θ = 3 - 1 = 2

⇒ tan2θ = 1

⇒ tanθ = 1 = tan 45º

∴ θ = 45º

∵ 180° = π radian

∴ 45° = π/180° × 45° = π/4 radian

∴ θ is π/4 radian