Practice!

Sample Problem

Find all solutions of tan2x+6tan x+5=0 on the interval [0, 2π).

Solution

tan2x+6tan x+5=0

(tan x+1)(tan x+5)=0 : now, use the inverse functions!

Tan x+1=0 , tan x=-1 , arctan(-1)=x

x=3π/4, 7π/4

Tan x+5=0 , tan x=-5 , arctan(-5)=x

But since x has to be in the interval [0, 2π),

x=arctan(-5)+π, arctan(-5)+2π