SOLUTION: Find all solutions of the equation in the interval [0,2π) 5 sqrt 3 tan x + 3 = 8 sqrt 3 tan x Thanks!

Algebra ->  Finance -> SOLUTION: Find all solutions of the equation in the interval [0,2π) 5 sqrt 3 tan x + 3 = 8 sqrt 3 tan x Thanks!      Log On


   

Question 1108678: Find all solutions of the equation in the interval [0,2π)
5 sqrt 3 tan x + 3 = 8 sqrt 3 tan x
Thanks!
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
5*sqrt(3)*tan(x) + 3 = 8*sqrt(3)*tan(x)


subtract 5*sqrt(3)*tan(x) from both sides.  You will get


3 = 3*sqrt(3)*tan(x)


1 = sqrt(3)*tan(x)  ====>  tan(x) = 1%2Fsqrt%283%29 = sqrt%283%29%2F3  ====>


there are two and only two solutions in the given interval:  x= pi%2F6   and  x = 7pi%2F6.