Find all real numbers in [0, 2π) that satisfy the equation.

cos 2x = √(2)/2

2x = 45,315,...

Follow for 2 periods to get values for x up to 360.

To find the real numbers in the interval [0, 2π) that satisfy the equation cos 2x = √(2)/2, we need to find the angles whose cosine value is equal to √(2)/2.

The cosine function represents the ratio of the adjacent side to the hypotenuse in a right triangle. By using the special angle properties, we can determine the values of x.

We know that cos(π/4) = √(2)/2, and the cosine function is positive in the first and fourth quadrants. Since we are restricted to the interval [0, 2π), the angles we must consider are:

x = π/4 (45 degrees)
x = 2π - π/4 = 7π/4 (315 degrees)

These are the only two solutions within the given interval.