Question

How do you find the value of `tan60` using the double angle identity?

Answer 1

`sqrt3`

Explanation:

Use trig identity:
`tan 2a = (2tan a)/(1 - tan^2 a)`
In this case:
`tan (60) = (2tan (30))/( 1 - tan^2 30)`
Trig table gives --> `tan 30 = sqrt3/3`--> `tan^2 30 = 3/9 = 1/3` -->
`(1 - tan^2 30) = 1 - 1/3 = 2/3`

`tan (60) = ((2sqrt3)/3)(3/2) = sqrt3`