Question

Cot A+ cot (60°+A) - cos (60°-A)=3(Cot3A)​

Answer 1

Step-by-step explanation:

1/tanA + 1/tan(60+A) - 1/tan(60-A)

1/tanA + 1-√3tanA/√3tanA - 1+√3tanA/√3 - tanA

1/tanA + (1-√3tanA)(1-√3tanA) - (1+√3tanA)(1+√3tanA)/ (1-√3tanA) (1+√3tanA)

1/tanA + √3 - tanA - 3tanA + √3tan^2A - √3 - tanA- 3tanA + √3tan^2A/ 3 - tan^2A

3 - 9tan^2A/ 3tanA - tan^3A

3(1-3tan^2A)/ 3tanA - tan^3A

3/ tan3A = 3Cot3A