Solve for x cot(x)- square root of 3=0

Problem

cot(x)−√(,3)=0

Solution

1. Isolate the cotangent term by adding √(,3) to both sides of the equation.

cot(x)=√(,3)

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

tan(x)=1/√(,3)

3. Rationalize the denominator to identify the standard value on the unit circle.

tan(x)=√(,3)/3

4. Identify the reference angle in the first quadrant where the tangent is √(,3)/3

x=π/6

5. Determine the general solution by adding multiples of the period of the tangent function, which is π

x=π/6+n*π

Final Answer

cot(x)−√(,3)=0⇒x=π/6+n*π

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