Question

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

Answer 1

x = ±π/6 +kπ . . . for any integer k

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