If Cos A = \({{9} \over 41}\), find cot A. 

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 4)
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  1. \({{9} \over 40}\)
  2. \({{41} \over 40}\)
  3. \({{40} \over 9}\)
  4. \({{9} \over 41}\)

Answer (Detailed Solution Below)

Option 1 : \({{9} \over 40}\)
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Detailed Solution

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Given:

Cos A = 9/41 

Formula used:

 cot A = cos A/sin A

Cos2 A + sin2 A = 1

Calculation:

Cos2 A + sin2 A = 1

⇒ ( 9/41)2 + sin2 A = 1

⇒  sin2 A = 1 - 81/1681

 ⇒ sin2 A = 1600/1681

⇒  sin A = 40/41

 cot A = cos A/sin A

 ⇒ cot A = 9/40

∴ Option 1 is the correct answer.

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