Question 141791
sec˛x – secx -2 =0

let z=sec x

z^2-z-2=0
(z-2)(z+1)=0

gives z=2 or z=-1

which is to say, sec x=2 or sec x=-1.

Now, sec x=1/(cos x)

When does 1/(cos x)=2 ???
When does 1/(cos x)=-1 ???

This is the same as asking when does cos x=1/2  or -1.
Interval [0, 2π) is a full unit circle except for the 360 degree mark.
Cos x=1/2 at 60 degrees and 300 degrees.
Cos x=-1 at 180 degrees.

In radians, x=π/3, x=π, x=5π/6.