Question

How do you solve `3tan^2x-1=0` for `0<=x<=360`?

Answer 1

`S={pi/6,(5pi)/6,(7pi)/6,(11pi)/6}`

Explanation:

`3tan^2x-1=0`
`3tan^2x=1`
`tan^2x=1/3`
`tanx=+-sqrt(1/3)=+-1/sqrt3`
`x=tan^-1(+-1/sqrt3)`
`x=pi/6+pin, x=-pi/6 +pin`
`n=0, x=pi/6, -pi/6`
`n=1, x= (7pi)/6,(5pi)/6`
`n=2, x= (13pi)/6, (11pi)/6`
`S={pi/6,(5pi)/6,(7pi)/6,(11pi)/6}`