How do you find the exact value of tanx-3cotx=0 in the interval 0<=x<360^@?

1 Answer
Nov 17, 2016

x\in {60^@, 120^@, 240^@, 300^@}

Explanation:

It goes as follows:
tan x-3cot x=0
tan x=3cot x
tan x=3\cdot 1/tan x
tan^2 x=3
tan x=sqrt 3 or tan x=-sqrt 3
x=60^@+k cdot 180^@ or x=120^@+k cdot 180^@ where k is an integer

Now we can simply list all solutions that fall between 0^@ and 360^@:
x\in {60^@, 120^@, 240^@, 300^@}

Note: at the very begining we should also include the domain of this equation; we want the tan x and cot x to exist so:
x\in\mathbb{R}\setminus {k cdot 90^@ | k " is integer"}
Fortunately enough, the solutions that we find fall into the domain.