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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.
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