Question

cosec theta+cot theta=√3,sin theta=?​

Answer 1

According to the problem:

Cosec θ + Cot θ = √3      -----(1)

We know that ,

Cosec² θ - Cot² θ = 1

( Cosec θ + Cot θ )(Cosec θ - Cot θ) =1

[ Since a² - b² = ( a + b ) ( a - b ) ]

( √3 ) ( Cosec θ - Cot θ ) = 1      [from (1) ]

Cosec θ - Cot θ = 1 / √3      -----(2)

On adding equations (1) and (2) we get,

    2Cosec θ = √3 + 1 /√3

⇒   2Cosec θ = ( 3 + 1 ) / √3

⇒  2Cosec θ  = 4 / √3

⇒ Cosec θ = 4 /2√3

⇒ Cosec θ = 2 / √3

⇒  Cosec θ = Cosec 60°

∴ θ = 60°

=> Sin θ = sin 60°

=> √3 / 2

Hope it helps :)

Answer 2

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Hope it helps to you...!!