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If tan θ + cot θ = 5, then the value of tanθ + cotθ + 2 tan60° is: 
1. 29 √3
2. 29
3. 25
4. 10 √3

1 Answer

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Correct Answer - Option 2 : 29

Given:

tan θ + cot θ = 5

Formula used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

tan θ + cot θ = 5

Squaring both sides

⇒ tan2θ + cot2θ + 2 tanθ cotθ = 25

⇒ tan2θ + cot2θ = 25 - 2

⇒ tan2θ + cot2θ = 23

tanθ + cotθ + 2 tan60°

⇒ 23 + 2 × (√3)2

⇒ 23 + 2 × 3

⇒ 29

∴ The required result = 29

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