What are solutions to the equation tan squared x minus three equals zero?

Answer 1

Solve for x, where tan² x - 3 = 0.

tan² x = 3; then,

sec² x = tan² x + 1 = 4,

sec x = ±2, and

cos x = 1 /sec x = ±½.

Now, we know that

sin 30° = ½; whence

cos 60° = ½.

Therefore, if 0 ≤ x < 2π, then

x = 60°, 120°, 240°, or 300°;

or, in radians,

x = ⅓π, ⅔π, 1⅓π, or 1⅔π.