√2 cos x = 1

So cos x = 1/√2

The principal solution is x = π/4

So solutions in the range 0 ≤ x ≤ 2π are

x = π/4, 7π/4

cosx = 1/sqrt(2)

x = pi/4, 7pi/4

You should learn your unit circle!

==> cos(x) = 1/√2

==> x = +/- arccos(1/√2) = 2π - π/4 or π/4 = 7π/4 or π/4