The problem at hand is to solve for x in the equation cos(2x) + sqrt(3)sin(2x) = sqrt(3).
To start solving this equation, we notice that sin(pi/3) = sqrt(3)/2 and cos(pi/3) = 1/2, these values come from standard trigonometric values that we know.
Using the identities for cosine and sine, also known as combination identities, we can rewrite our given equation. We get sqrt(3) * sin(pi/3) * cos2x + sin(pi/3) * sin2x = sqrt(3).
Simplifying this, it can be expressed as: sin(pi/3) * sin2x + sqrt(3) * cos(pi/3) * cos2x = sqrt(3).
Looking at it now, we can recognize this form as the formula for cos(a - b) where a is pi/3, our known value, and b is 2x, our unknown to solve for. This leaves us with cos(pi/3 - 2x) = sqrt(3).
We know that cos(pi/6) = sqrt(3)/2, using this we transform the equation into pi/3 - 2x = pi/6.
Rearranging to solve for x, we subtract and divide to end up with x = pi/12.
Hence, the solution to the given equation is x = pi/12.