If tan A + cot A = 2, then the value of 2(tan2 A + cot2 A) is :

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)
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  1. 1
  2. 4
  3. 2
  4. 3

Answer (Detailed Solution Below)

Option 2 : 4
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Detailed Solution

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Given:

tan A + cot A = 2

Calculation:

According to the question,

we have tan A + cot A = 2

Squaring both sides, we get

⇒ (tan A + cot A)2 = (2)2

⇒ tan2 A + cot2 A + 2(tan A)(cot A) = 4

⇒ tan2 A + cot2 A + 2(tan A)(1/tan A) = 4

⇒ tan2 A + cot2 A + 2 = 4

⇒ tan2 A + cot2 A = 2

Now,

2(tan2 A + cot2 A) = 2 × 2

⇒ 4

∴ The value of 2(tan2 A + cot2 A) is 4.

Shortcut Trick We can go with the value-putting method,

If we put A = 45° it satisfies the equation tan A + cot A = 2, so

2(tan2 A + cot2 A) 

⇒ 2(1 + 1)

⇒ 4

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