Finding the exact solution over the indicated interval?

Question

4tan^2x - 3/cos^2x = 0 0<x<360

Answer 1

4tan²θ - 3 / cos²θ = 0

4(sin²θ / cos²θ) - 3 / cos²θ = 0

(4sin²θ - 3) / cos²θ = 0

4sin²θ - 3 = 0

sin²θ = 3/4

sinθ = ±√3/2

θ = 60°, 120°, 240°, 300°

Answer 2

First, because cos^2x is not zero, let's multiply both sides of the equation by cos^2x.

4sin^2x - 3 = 0

sin^2x = 3/4.

sinx = ±sqrt(3)/2. Thus, x = pi/3,2pi/3,4pi/3, and 5pi/3, as we move counterclockwise around the unit circle.