Find the value of sin2 θ + cosec2 θ.

If sin θ + cosec θ = 2, find the value of sin² θ + cosec² θ.

Answer :

sin θ + cosec θ = 2

⇒ sin θ + 1/sin θ = 2

sin² θ + 1 = 2 sin θ

⇒ sin² θ – 2 sin θ + 1 = 0

(sin θ – 1)² = 0

⇒ sin θ – 1 = 0

⇒ sin θ = 1

sin² θ + cosec² θ = sin² θ + 1/sin² θ

= 1² + 1/1²

= 1 + 1/1

= 1 + 1

= 2

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