Solve 4tan^2x-1=tan^2x

Question

Find all solutions between [0,2π), please.

Answer 1

4 tan² x - 1 = tan² x

 

3 tan² x = 1

 

tan² x = 1/3

 

tan x = ±1/√3

 

x = ±π/6 + kπ ; k∈Z

 

In the range [0,2π) are only four values

 

They are π/6, 5π/6, 7π/6, 11π/6