Find all solutions of given equation

2cosx-1=0

2cosx=1

cosx=1/2

x=cos∧-1 (1/2)

x=60degrees or 360-60=300degrees

depending on your limits if in radians pi/3 and 5pi/3

There are an infinite number of solutions, so I don't plan to list them all.

I'll list two of them, and then describe how to get all of the rest.

You said that 2cos (x) - 1 = 0

Add 1 to each side: 2cos (x) = 1

Divide each side by 2: cos (x) = 1/2

The angles whose cosine is 1/2 are 60 degrees, 300 degrees,

and any multiple of 360 degrees added to either of those.