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

Problem

cot(x)=√(,3)

Solution

1. Identify the reciprocal relationship between the cotangent and tangent functions to rewrite the equation.

tan(x)=1/cot(x)

2. Substitute the given value of cot(x) into the reciprocal identity.

tan(x)=1/√(,3)

3. Determine the reference angle by finding the value of x in the first quadrant where the tangent is 1/√(,3)

x=π/6

4. Apply the general solution formula for the tangent function, which has a period of π

x=π/6+n*π

Final Answer

cot(x)=√(,3)⇒x=π/6+n*π,n∈ℤ

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