If cot B = 9, then what will be the value of sec2 B?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 3)
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  1. 98/81
  2. 92/81
  3. 42/81
  4. 82/81

Answer (Detailed Solution Below)

Option 4 : 82/81
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Detailed Solution

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Given:

cot B = 9

Concept used:

1. cosec2 θ - cot2 θ = 1

2. sin2 θ + cos2 θ = 1

3. sin θ = 1/cosec θ

4. cos θ = 1/sec θ

Calculation:

cot B = 9

⇒ cot2 B = 81

⇒ 1 + cot2 B =  1 + 81

⇒ cosec2 B = 82

⇒ sin2 B = 1/82

⇒ 1 - sin2 B = 1 - 1/82

⇒ cos2 B = 81/82

⇒ sec2 B = 82/81

∴ The value of sec2 B is 82/81.

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