**If sin θ + cosec θ = 3 1/3, find the value of sin**^{2} θ + cosec^{2} θ.

^{2}θ + cosec

^{2}θ.

**Answer :**

sin θ + cosec θ = 3 1/3 = 10/3

By squaring on both sides

(sin θ + cosec θ)^{2} = (10/3)^{2}

Expanding using formula (a + b)^{2} = a^{2} + b^{2} + 2ab

sin^{2} θ + cosec^{2} θ + 2 sin θ cosec θ = 100/9

We know that sin θ = 1/cosec θ

sin^{2} θ + cosec^{2} θ + (2 sinθ× 1/sin θ) = 100/9

sin^{2} θ + cosec^{2} θ + 2 = 100/9

⇒ sin^{2} θ + cosec^{2} θ = 100/9 – 2

Taking LCM

sin^{2} θ + cosec^{2} θ = (100 – 18)/9 = 82/9

sin^{2} θ + cosec^{2} θ = 9 1/9

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