**If sin θ + cosec θ = 2, find the value of sin**^{2} θ + cosec^{2} θ.

^{2}θ + cosec

^{2}θ.

**Answer :**

sin θ + cosec θ = 2

⇒ sin θ + 1/sin θ = 2

sin^{2} θ + 1 = 2 sin θ

⇒ sin^{2} θ – 2 sin θ + 1 = 0

(sin θ – 1)^{2} = 0

⇒ sin θ – 1 = 0

⇒ sin θ = 1

sin^{2} θ + cosec^{2} θ = sin^{2} θ + 1/sin^{2} θ

= 1^{2} + 1/1^{2}

= 1 + 1/1

= 1 + 1

= 2

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