Solve the following equation: `tan^2x+(1-sqrt(3))tanx-sqrt(3)=0`

Answer

`x=npi +pi/3, n in Z or x=mpi - pi/4; m in Z`

Explanation

`tan^(2)x + tan x - sqrt3 tan x - sqrt3 = 0`
or `(tan x - sqrt3) (tan x + 1) = 0`
or `tan x = sqrt3 or tan x = -1`
`tan x = sqrt3 = tan (pi//3)`
`rArr x = n pi + pi//3, n in Z`
and `tan x = - 1 = tan (- pi//4)`
`rArr x = m pi - pi//4, m in Z`