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

  x = ±π/6 +kπ . . . for any integer k

Step-by-step explanation:

Solving for x, we have ...

  1 = 3tan(x)² . . . . . add 3tan(x)²

  ±√(1/3) = tan(x) . . . divide by 3, take the square root

  x = arctan(±√(1/3)) +kπ . . . . use the inverse function to find x

  x = ±π/6 +kπ

ou would have 12 of each