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

Problem

tan(x/2)=√(,3)/3

Solution

1. Identify the value on the right side of the equation as a known trigonometric ratio.

√(,3)/3=1/√(,3)

2. Determine the reference angle for which the tangent function equals 1/√(,3)

tan(π/6)=1/√(,3)

3. Set up the general solution for the tangent equation, noting that the period of tangent is π

x/2=π/6+n*π

4. Isolate x by multiplying both sides of the equation by 2

x=2*(π/6+n*π)

5. Simplify the expression to find the final general solution, where n is any integer.

x=π/3+2*n*π

Final Answer

tan(x/2)=√(,3)/3⇒x=π/3+2*n*π

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