If tan θ + cot θ = 12, then tan2 θ + cot2 θ is:

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 4)
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  1. 66
  2. 128
  3. 142
  4. 132

Answer (Detailed Solution Below)

Option 3 : 142
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Detailed Solution

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Given:

tan θ + cot θ = 12

Formula used:

(x + 1/x)2 = (x2 + 1/x2) + 2

cot θ = 1/tan θ

Calculation:

tan θ + cot θ = 12

tan θ + 1/tan θ = 12

Square both sides:

(tan θ + 1/tan θ)2 = 122

tan2 θ + 1/tan2 θ = 144 - 2 

tan2 θ + cot2 θ = 142

∴ Option 3 is the correct answer.

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