First, isolate the cosine term by dividing both sides by 2:

cos(x-π/6) = √3 / 2

Now, recall that cos(π/6) = √3 / 2. Thus, we can rewrite the equation as:

cos(x-π/6) = cos(π/6)

Since the cosine function is an even function, we have:

x-π/6 = π/6 + 2kπ, where k is an integer

Now, solve for x:

x = π/6 + π/6 + 2kπ

x = π/3 + 2kπ

Therefore, the general solution for the equation 2cos(x-π/6) = √3 is:

x = π/3 + 2kπ, where k is an integer.