Using the Formal, tan2=2tanA÷1-tansquareA, Find the value of tan 60, it being given that 30=1÷root3

Using the Formal, tan2=2tanA÷1-tansquareA, Find the value of tan 60,

1.	Using the Formal, tan2=2tanA÷1-tansquareA, Find the value of tan 60, it being given that 30=1÷root3
Answer» Given Formula : tan2A = 2 tan A / 1 - tan²A Also, tan30 = 1/√3Required to find : tan60Now, Let A = 30 , 2A = 60° tan2A = 2tanA / 1 - tan²A tan60 = 2(tan30 ) / 1 - ( tan²30)tan60 = 2(1/√3) / 1 -( 1/√3)²tan60 = 2/√3 / 1 - 1/3tan60 = 2/√3 / 2/3 tan60 = 2/√3 * 3/2 tan60 = √3 Therefore , tan60 = √3