Question

Using formula tan2a=2tana/1-tana×tanafind the value of 60 it being given that tan 30's value

Answer 1

Given Formula : tan2A = 2 tan A / 1 - tan²A

Also, tan30 = 1/√3

Required to find : tan60

Now,

Let A = 30 , 2A = 60°

tan2A = 2tanA / 1 - tan²A

tan60 = 2(tan30 ) / 1 - ( tan²30)

tan60 = 2(1/√3) / 1 -( 1/√3)²

tan60 = 2/√3 / 1 - 1/3

tan60 = 2/√3 / 2/3

tan60 = 2/√3 * 3/2

tan60 = √3

Therefore , tan60 = √3