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If θ is a positive acute angle and cosec θ + cot θ = √3 , then the value of cosec θ is
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1 √3 - √3
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2 √3 - 1
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Correct Option: C
cosecθ + cotθ = 3 ...(i)
cosec²θ – cot²θ = 1
⇒ (cosecθ + cotθ) (cosecθ – cotθ) = 1
| ⇒ cosecθ - cotθ = | ....(ii) | √3 |
| ∴ cosecθ + cotθ + cosecθ – cotθ = √3 + | √3 |
| ⇒ 2 cosecθ = | √3 |
| ⇒ cosecθ = | = | 2√3 | √3 |
