To solve the equation 2cos(5x) = √3, we first need to isolate the cosine function by dividing both sides by 2:

cos(5x) = √3 / 2

Next, since the cosine function is equal to √3/2 at π/6 (30 degrees) and 11π/6 (330 degrees), we can set up the equation:

5x = π/6 + 2nπ, where n is an integer
5x = 11π/6 + 2nπ, where n is an integer

Now, solve for x:

x = π/30 + (2nπ) / 5, where n is an integer
x = 11π / 30 + (2nπ) / 5, where n is an integer

These are the general solutions for the equation 2cos(5x) = √3.