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

Problem

tan(x/2)=√(,3)

Solution

1. Identify the basic trigonometric equation form tan(θ)=a where θ=x/2 and a=√(,3)

2. Determine the principal value for θ by finding the angle whose tangent is √(,3)

x/2=π/3

3. Apply the general solution formula for the tangent function, which has a period of π

x/2=π/3+n*π

where n is any integer.

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

x=2*(π/3+n*π)

5. Distribute the 2 to simplify the expression for the general solution.

x=(2*π)/3+2*n*π

Final Answer

tan(x/2)=√(,3)⇒x=(2*π)/3+2*n*π

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