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.