tan^(2)(x)-3tan(x)-1=0

Question

for 0<=x<=2\pi in degrees

Answer 1

let y= tan(x)

y^2 -3y -1 =0

y^2 -3y + (3/2)^2 = 1 + (3/2)^2

(y - 3/2)^ 2 = 13/4

y = 3/2 + or - (1/2)sqr13= 1.5 + or - 1.803 = -0.303 or 3.303

tanx = -0.303 or + 3.303

x = the inverse tangent of -0.303 or 3.303

x = 73.2 degrees or 106.8 or 196.9 or 343.1 degrees