Question

Find all solutions in the interval [0, 2π).

7 tan^3x - 21 tan x = 0

A) pi/3, 2pi/3, 4pi/3, 5pi/3
B) 0, pi/5, π, 6pi/5
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
D) 0, pi/3, π, 4pi/3

Answer 1

Let tan x = a
7 tan^3 x - 21 tan x = 0 becomes
7a^3 - 21a = 0
7a(a^2 - 3) = 0
a = 0 or a^2 - 3 = 0
a = 0 or a^2 = 3
a = 0 or a = + or - √3

tan x = 0, tan x = √3, tan x = -√3
x = 0, pi, pi/3, 4pi/3, 2pi/3, 5pi/3