Solve for x cot(3x) = square root of 3

Problem

cot(3*x)=√(,3)

Solution

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

tan(3*x)=1/√(,3)

2. Identify the reference angle for which the tangent is 1/√(,3) which is π/6 (or 30.

3*x=π/6+n*π

3. Isolate x by dividing the entire expression by 3

x=π/18+(n*π)/3

4. Define the variable n as any integer to represent the general solution.

n∈ℤ

Final Answer

cot(3*x)=√(,3)⇒x=π/18+(n*π)/3

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