solve for cos^2x=secx
note: cos square root of 2 x.
cos^2x means cosx squared, or (cosx)^2 , not square root or √cosx !
I will assume you meant (cosx)^2
cos^2 x=secx
cos^2 x= 1/cosx
cos^3 x = 1
cosx = 1
from the graph, we know cos 0 = 1, cos 2π = 1
so x = 0, 2π