Question

find all real solutions to tan^2x=3

Answer 1

take sqrt

tan x = +-sqrt(3)

next take inverse tangent, or use a unit circle
--> tan(pi/3) = sqrt3
-->tan(4pi/3) = sqrt3
--> tan(2pi/3) = -sqrt3
--> tan(5pi/3) = -sqrt3

notice pi/3 + pi = 4pi/3
2pi/3 + pi = 5pi/3

All real solutions:
\[x = \frac{\pi}{3} + n \pi, \frac{2\pi}{3} + n \pi\]

Answer 2

thank you!

Answer 3

yw