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Find the value of (1 - 3 tan2 20°)/(3 tan 20° - tan3 20°)

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Best answer
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. 

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