Please Help! Pre-Calculus and Trigonometry.

Question

Give exact values. Both in degrees and radians.

tan²x - 1 = 0

Answer 1

tan**2x - 1 = 0

Factoring the difference of two squares:

(tanx + 1) * (tanx - 1) = 0

so either tanx = -1 or tan x = 1, which occurs when |sin x| = |cos x|

this occurs at 45, 135, 225, 315, etc or 45 + 90 * n degrees, where n = 0, 1, 2, 3, ...

or pi/4, 3*pi/4, 5*pi/4, 7*pi/4 or pi/4 + pi/2 * n, where n = 0, 1, 2,3, ...