Find all solutions of the equation in the interval [0, 2π).

Question

3tan^2x-1=0

Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.

Answer 1

3tan^2x-1=0

tan^2x=1/3

tanx =±1/sqrt(3)

tanx =1/sqrt(3)

tanx = tan(π/6)

x=nπ+π/6

n=0,x=π/6

n=1,x=π+π/6=7π/6

tanx =-1/sqrt(3)

tanx = tan(-π/6)

x=nπ-π/6

n=1,x=π-π/6=5π/6

n=2,x=2π-π/6=11π/6

n=π/6,5π/6,7π/6, and 11π/6.