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 the general solution by considering the quadrants where cosine is positive (Quadrants I and IV) and the periodicity of the cosine function (2*π*n.

x=π/6+2*π*n

x=−π/6+2*π*n

Final Answer

x=±π/6+2*π*n

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