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Find all solutions in the interval [0,2pi): tan^2x + (sqrt3-1)tanx-sqrt3 = 0

This is for my trig class. Thanks for the help!

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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Factor,
(tan x + sqrt3)(tan x - 1) = 0
tan x = -sqrt3, => x = 2pi/3, 5pi/3
or
tan x = 1, => x = pi/4, 5pi/4
Answer: x = pi/4, 2pi/3, 5pi/4, 5pi/3