Question

Find all solutions in the interval [0, 2π). 7 tan^3x - 21 tan x = 0

Answer 1

To solve this problem, the first thing we can do is to take out 7 tan (x) from the whole equation, this results in simplification:

7 * tan (x) * (tan (x)^2 - 3) = 0 

Therefore the initial roots are taken from:

tan (x) = 0

Calculating for x:

x = 0, pi

 

The other roots can be taken from:

(tan (x)^2 - 3) = 0 

Calculating for x:

tan (x)^2 = 3

tan (x) = ± sqrt (3)  

x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3 

 

Therefore the solutions are:

0 , pi, pi/3 , 2pi/3 , 4pi/3 , 5pi/3