Use the identity
Multiply through by
Use the principle of square roots:
The solutions are all angles with a reference angle of , , ,
Edwin
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website! Find all values of t in the interval [0,2π] if cot t-3tan t=0
---------------
cot(t) - 3tan(t) = 0
Multiply by tan(t)
1 - 3tan^2 (t) = 0
3tan^2(t) = 1
tan^2(t) = 1/3
tan(t) = ± sqrt(3)/3
t = 30 degs, 210 degs
t = pi/6, 7pi/6 radians