Solve for x 2cos(x)- square root of 3=0

Problem

2*cos(x)−√(,3)=0

Solution

1. Isolate the trigonometric term by adding √(,3) to both sides of the equation.

2*cos(x)=√(,3)

2. Divide both sides by 2 to solve for cos(x)

cos(x)=√(,3)/2

3. Identify the reference angle in the first quadrant where the cosine value is √(,3)/2

x=π/6

4. Determine all solutions within the standard interval [0,2*π) by considering the quadrants where cosine is positive (Quadrants I and IV).

x=π/6

x=2*π−π/6=(11*π)/6

5. Generalize the solution by adding multiples of the period 2*π where n is any integer.

x=π/6+2*n*π

x=(11*π)/6+2*n*π

Final Answer

x=π/6+2*n*π,(11*π)/6+2*n*π

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