Solve for x cot(3x)=1

Problem

cot(3*x)=1

Solution

1. Rewrite the equation in terms of the tangent function using the identity cot(θ)=1/tan(θ)

tan(3*x)=1

2. Determine the general solution for the angle 3*x by finding the inverse tangent of 1

3*x=arctan(1)+n*π

3. Evaluate the principal value of arctan(1) which is π/4

3*x=π/4+n*π

4. Isolate x by dividing the entire expression by 3

x=π/12+(n*π)/3

Final Answer

cot(3*x)=1⇒x=π/12+(n*π)/3,n∈ℤ

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