Question

If sin θ + cosec θ = 2, then the value of sin² θ + cosec² θ is:
1. 4
2. 8
3. 2
4. 1

Answer 1

Correct Answer - Option 3 : 2

Given:

sinθ + cosecθ = 2

Formula Used:

cosecθ = 1/sinθ

Calculation:

Let sinθ = x

⇒ sinθ + cosecθ = x + 1/x = 2

⇒ (x + 1/x)² = 2²

⇒ x² + 2 + 1/x² = 4

⇒ x² + 1/x² = 2

∴ sin²θ + cosec²θ = 2