To solve the equation 2cos(x)^2 - 1 = 0, we first need to isolate the cosine term.

Adding 1 to both sides of the equation, we get:

2cos(x)^2 = 1

Next, divide by 2 to solve for cos(x)^2:

cos(x)^2 = 1/2

Taking the square root of both sides, we get:

cos(x) = ±√(1/2)

Since cosine is positive in the first and fourth quadrants, the solutions for x will be:

x = ±π/4 + 2nπ , where n is an integer.

Therefore, the complete solution to the equation 2cos(x)^2 - 1 = 0 is:

x = ±π/4 + 2nπ, where n is an integer.