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

Problem

2*cos(x/2)=√(,3)

Solution

1. Isolate the trigonometric function by dividing both sides of the equation by 2

cos(x/2)=√(,3)/2

2. Identify the reference angle for which the cosine value is √(,3)/2 which is π/6 (or 30.

x/2=±π/6+2*k*π

3. Solve for x by multiplying the entire equation by 2 to isolate the variable.

x=±π/3+4*k*π

4. Define the integer constant k to represent all possible solutions in the general form.

k∈ℤ

Final Answer

x=±π/3+4*k*π

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