Final answer:
The general solutions for the equation 2cos(x) - √3 = 0 are x = π/6 + 2nπ and x = 11π/6 + 2nπ for any integer n.
Step-by-step explanation:
To solve the mathematical problem completely, we need to find all solutions for the equation given by 2cos(x) - √3 = 0. Solving for cos(x), we have cos(x) = √3/2.
This value corresponds to an angle with a reference angle of π/6 in the unit circle, which gives us two solutions in the interval [0, 2π]: x = π/6 and x = 11π/6.
However, since the cosine function is periodic with a period of 2π, we can find a general solution for x by adding any integer multiple of 2π to these solutions.
Hence, the general solutions are x = π/6 + 2nπ and x = 11π/6 + 2nπ for any integer n.