Question

How do you solve `tan^2x-3=0` and find all solutions in the interval `[0,2pi)`?

Answer 1

`S={pi/3, (2pi)/3, (4pi)/3,(5pi)/3}`

Explanation:

`tan^2x-3=0`
`tan^2x=3`
`tan x=+- sqrt3`
`x=tan^-1(+-sqrt3)`
`x=pi/3 + pin, x=-pi/3+pin`
`n=0, x= pi/3, -pi/3`
`n=1, x=(4pi)/3, (2pi)/3`
`n=2, x=(7pi)/3,(5pi)/3`
`S={pi/3, (2pi)/3, (4pi)/3,(5pi)/3}`