Question

How do you find the general solutions for `Tan x - 3cotx = 0`?

Answer 1

Solve tan x - 3cot x = 0

Ans: `pi/3 and (2pi)/3`

Explanation:

`tan x - 3/tan x = 0`
`tan^2 x - 3 = 0` (condition tan x not zero)
`tan^2 x = 3` --> `tan x = +- sqrt3`

a. `tan x = sqrt3` --> `x = pi/3`
b. `tan x = -sqrt3` --> `x = (2pi)/3`

Extended answers:
`x = pi/3 + kpi`
`x = (2pi/3) + kpi`