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
tan2 θ + cot2 θ + 2 tan2 60°
⇒ 23 + 2 × (√3)2
⇒ 23 + 2 × 3
⇒ 29
∴ The required result = 29