3tanx-2cotx=3

Question

find all values of x

Answer 1

Let 

 

y = tan(x)

 

Then

 

3y - 2/y = 3

 

3y² - 2 = 3y

 

3y² - 3y - 2 = 0

 

Solve this quadratic equation for y (2 solutions), and then

 

x = arctan(y)

 

Keep in mind that arctan(y) is multi-valued.