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

Problem

tan(x/2)=√(,3)

Solution

1. Identify the basic angle where the tangent function equals √(,3)

tan(θ)=√(,3)⇒θ=π/3

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

x/2=π/3+n*π

3. Isolate the variable x by multiplying both sides of the equation by 2

x=2*(π/3+n*π)

4. Distribute the 2 to find the final general solution, where n is any integer.

x=(2*π)/3+2*n*π

Final Answer

tan(x/2)=√(,3)⇒x=(2*π)/3+2*n*π

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