Question

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.

Answer 1

no!

why don't you factor it with the secant as is
sec^2 x + secx - 2 = 0
(secx + 2)(secx-1) = 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)

Answer 2

The answers in the back of my book are pi/3,pi, and 5pi/3