Solve for x cot(x)=1

Problem

cot(x)=1

Solution

1. Rewrite the equation using the reciprocal identity for the cotangent function.

tan(x)=1/cot(x)

2. Substitute the given value into the identity to find the value of the tangent function.

tan(x)=1/1

tan(x)=1

3. Identify the reference angle in the first quadrant where the tangent is equal to 1

x=π/4

4. Determine the general solution by adding the period of the tangent function, which is π multiplied by an integer n

x=π/4+n*π

Final Answer

cot(x)=1⇒x=π/4+n*π,n∈ℤ

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