solve for all 0≤x≤2π

Question

1. √3 tan x sec x+2tan x=0

Answer 1

start by factoring out tan x on the left side

tanx(sqroot 3secx +2)=0 so have 2 solutions

tanx = 0 x =0, pi, 2pi. and

sqrooot3secx+2 =0

secx= -2/sqroot 3 which is equivalent to

cosx = -sqroot 3/2 x= 5pi/6 and 7pi/68