PreCalculus
posted by Sharon .
Find the solutions for sec^2x+secx=2 that fit into the interval [0, 2pi]
I figured out that pi/3 (after factoring and switching things around) was a solution, but then I got stuck on cos x = 1/3.

no!
why don't you factor it with the secant as is
sec^2 x + secx  2 = 0
(secx + 2)(secx1) = 0
secx = 2 or secx = 1
cosx = 1/2 or cosx = 1
from cosx = 1/2, x = 120º (2pi/3) or 240º (4pi/3)
or
from cosx = 1, x = 0 or 360º (0 or 2pi) 
The answers in the back of my book are pi/3,pi, and 5pi/3