Question

Which of the following is a solution to 3tan^3x=tanx? PLEASE HELP

Answer 1

Answer:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Explanation:
3 tan³x = tan x
3 tan³x - tan x = 0
tan x (3 tan²x - 1) = 0
either tan x = 0
This means that:
x = 0 , π or 2π ...........> I

or 3 tan²x - 1 = 0
This means that:
3 tan²x = 1
tan²x = $\frac{1}{3}$
tan x = ± $\frac{1}{ \sqrt{3}}$
at tan x = $\frac{1}{ \sqrt{3}}$
x = π/6 or 7π/6 ...................> II
at tan x = - $\frac{1}{ \sqrt{3}}$
x = 5π/6 or 11π/6 ..............> III

From I, II and III, the solutions for x would be:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Hope this helps :)