What are all the exact solutions of - 3tan^2x+1=0? Give your answers in radians.

x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 - 3 tan^2 (x) = 0

Subtract 1 from both sides:

-3 tan^2 (x) = - 1

Divide both sides by - 3:

tan^2 (x) = 1/3

Take the square root of both sides:

tan (x) = 1/sqrt (3) or tan (x) = - 1/sqrt (3)

Take the inverse tangent of both sides:

x = π n_1 + π/6 for n_1 element Z

or tan (x) = - 1/sqrt (3)

Take the inverse tangent of both sides:

Answer: x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z