Which of the following is a solution to 3tan^3x=tanx?PLEASE HELP
Accepted Solution
A:
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 = [tex] \frac{1}{3} [/tex] tan x = ± [tex] \frac{1}{ \sqrt{3}} [/tex] at tan x = [tex] \frac{1}{ \sqrt{3}} [/tex] x = π/6 or 7π/6 ...................> II at tan x = - [tex] \frac{1}{ \sqrt{3}} [/tex] 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