Values of t? Calc help?

Question

Find all the values of t in the interval [0,2π] if tan t-3 cot t=0.

Not sure what the steps are. Can someone please help! :]

10 points

Answer 1

what is the punctuation between the tan and the cot?

Answer 2

tant-3cot t=0

sin(t)/cos(t) = 3 *cos(t)/sin(t)

sin(t) ^2 = 3 cos(t)^2

tan(t) ^2= 1/3

tan(t) = 1/sqr(3)

get t

Answer 3

tan t - 3/tan t = 0

tan^2 t -3 = 0

tan^2 t = 3

tan t = +/- sqrt(3)

t = pi/3, 2pi/3, 4pi/3, 5pi/3