Question

12 cot2(x) = 4 find all values of x in the interval [0, 2π] that satisfy the equation

Answer 1

$cot^2x = 4/12 \\ cot^2x = 1/3 \\ tan^2x = 3 \\ tan(x)= +- \sqrt{3}$

so,  $x= \pi/3 \\ x = \pi - \pi/3 = 2\pi/3 \\ x = \pi + \pi/3 = 4\pi/3 \\ x = 2\pi - \pi/3 = 5\pi/3$