Solve for x tan(x/2-pi/4)=1

Problem

tan(x/2−π/4)=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 value.

x/2−π/4=π/4+n*π

2. Isolate the term containing x by adding π/4 to both sides of the equation.

x/2=π/4+π/4+n*π

3. Simplify the constant terms on the right side.

x/2=π/2+n*π

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

x=π+2*n*π

5. Factor out the common term π to express the solution in a standard form, where n is any integer.

x=π*(1+2*n)

Final Answer

tan(x/2−π/4)=1⇒x=π*(2*n+1)

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