Question

Find all solutions in the interval [0,360°)
tan2θ−√3tanθ=0

Answer 1

tan 2x = sqrt3 tan x
**tan 2x = 2 tan x / 1-tan(x)^2

2 tanx = sqrt3 tanx(1-tanx^2)
sqrt3 tanx^3 +(2-sqrt3)tanx = 0
tanx (sqrt3 tanx^2 +(2-sqrt3)) =0

tanx = 0 --> x =0,180
sqrt3 tanx^2 = -(2-sqrt3)
tanx = sqrt((sqrt3 -2)/sqrt3) = sqrt(1 - (2/sqrt3))
1 - 2/sqrt3 < 0
x has no real solutions