Question

How do you solve for x in: `tan^2 x - 3 tan x - 4 = 0`?

Answer 1

Let `k=tan(x)`
then
`tan^2(x) -3tan(x)-4 = 0`
becomes
`k^2-3k-4=0`

`(k-4)(k+1) = 0`

So we are looking for
`k=4` or `k=-1`
that is, for
`tan(x) = 4` or `tan(x)=-1`

`x = arctan(4)`
or
`x= arctan(-1) = -pi/4 +n(pi)` for all `n epsilon ZZ`