MATH SOLVE

2 months ago

Q:
# 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

Hope this helps :)

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

Hope this helps :)