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

1 Answer
Nghi N.
Aug 25, 2015

Solve tan x - 3cot x = 0

Ans: pi/3 and (2pi)/3π3and2π3

Explanation:

tan x - 3/tan x = 0tanx−3tanx=0
tan^2 x - 3 = 0tan2x−3=0 (condition tan x not zero)
tan^2 x = 3tan2x=3 --> tan x = +- sqrt3tanx=±√3

a. tan x = sqrt3tanx=√3 --> x = pi/3x=π3
b. tan x = -sqrt3tanx=−√3 --> x = (2pi)/3x=2π3

Extended answers:
x = pi/3 + kpix=π3+kπ
x = (2pi/3) + kpix=(2π3)+kπ

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