Question

How do you solve: `tan^2 x - 1 = 0` for solutions up to 2pi?

Answer 1

`x in {pi/4,(3pi)/4,(5pi)/4,(7pi)/4}`

Explanation:

If `tan^2(x) -1 =0`
then
`tan^2(x) = 1`
and
`tan(x) = +-1`

Within the domain `[0,2pi]`
this occurs at
`x = pi/4`, `x=(3pi)/4`, `x=(5pi)/4`, and `x=(7pi)/4`
(from basic definition of `tan`)