Correct Answer - Option 2 : 1/√3
Concept Used:
tan 3θ = (3 tan θ - tan3 θ)/(1 - 3 tan2 θ)
Cot 60° = 1/√3
Calculation:
1/tan 3θ = (1 - 3 tan2 θ)/(3 tan θ - tan3 θ)
⇒ (1 - 3 tan2 20°)/(3 tan 20° - tan3 20°) = 1/tan (3 × 20°)
⇒ 1/tan 60°
⇒ Cot 60°
⇒ 1/√3
∴ The value of (1 - 3 tan2 20°)/(3 tan 20° - tan3 20°) is 1/√3.