Question

HELP PLEEASE!!!
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

0 certainly works so forget the first answer
you might try factoring as
\[7\tan(x)(\tan^2(x)-3)\] as a first step
then go to
\[\tan^2(x)=3\]and so
\(\tan(x)=\sqrt{3}\) or \(\tan(x)=-\sqrt{3}\)

Answer 2

So in that case it would be:
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3

Answer 3

that looks good to me

Answer 4

Alright thanks