Question

Using the formula, tan 2A =`(2 tan A )/(1- tan^2 A)` find the value of tan 60⁰, it being given that tan 30⁰ = `1/sqrt(3)`. 

Answer 1

A = 30⁰ 
⇒ 2A = 2 × 30⁰ = 60⁰ 
By substituting the value of the given T-ratio, we get:

tan 2A = `(2 tan A )/(1- tan^2 A)`

`⇒ tan 60^0 = (2  tan 30^0)/(1- tan^2 30^0) = (2xx (1/sqrt(3)))/(1-(1/sqrt(3))^2 ` =` ((2/sqrt(3)))/(1-1/3) = ((2/sqrt(3)))/(2/3) = (2/sqrt(3))= 3/2 = sqrt(3) `

∴tan` 60^0 = sqrt(3)`.