Solve for x tan(x/2+pi/3)=1

Problem

tan(x/2+π/3)=1

Solution

1. Identify the general solution for the tangent function. Since tan(θ)=1 when θ=π/4+n*π we set the argument of the tangent function equal to this general form.

x/2+π/3=π/4+n*π

2. Isolate the term containing x by subtracting π/3 from both sides of the equation.

x/2=π/4−π/3+n*π

3. Find a common denominator for the fractions on the right side to simplify the expression.

x/2=(3*π)/12−(4*π)/12+n*π

x/2=−π/12+n*π

4. Solve for x by multiplying the entire equation by 2

x=2*(−π/12+n*π)

x=−π/6+2*n*π

Final Answer

tan(x/2+π/3)=1⇒x=−π/6+2*n*π,n∈ℤ

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