Solve for x tan(3x)=1

Problem

tan(3*x)=1

Solution

1. Identify the general solution for the tangent function. The equation tan(θ)=a has the general solution θ=arctan(a)+n*π where n is an integer.

2. Determine the principal value of arctan(1) Since tan(π/4)=1 the principal value is π/4

3. Set up the equation for the argument 3*x using the general solution formula.

3*x=π/4+n*π

4. Solve for x by dividing both sides of the equation by 3

x=π/12+(n*π)/3

Final Answer

tan(3*x)=1⇒x=π/12+(n*π)/3

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