यदि cosec θ + cot θ = \(\frac{3}{2}\) है, तब cosec θ का मान ज्ञात कीजिए। 

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 3)
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  1. \(\frac{13}{12}\)
  2. \(\frac{3}{2}\)
  3. \(\frac{11}{12}\)
  4. \(\frac{9}{13}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{13}{12}\)
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दिया गया है : 

cosec θ + cot θ = 3/2 

प्रयुक्त सूत्र :

cosec2θ - cot2θ = (cosec θ + cot θ)(cosec θ - cot θ) = 1 

गणना :

cosec θ + cot θ = 3/2 ....(1)

cosec θ - cot θ = 2/3     ....(2)

समीकरण 1 और 2 को हल करने पर, हमें प्राप्त होता है: 

2cosec θ = 13/6 

⇒ cosec θ  = 13/12  

∴ cosec θ का मान 13/12 है। 

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