Solve for x cot(x)-1=0

Problem

cot(x)−1=0

Solution

1. Isolate the trigonometric function by adding 1 to both sides of the equation.

cot(x)=1

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

tan(x)=1

3. Determine the reference angle by finding the value of x in the first quadrant where the tangent is 1.

x=π/4

4. Identify the general solution by considering the period of the tangent function, which is π

x=π/4+n*π

Final Answer

cot(x)−1=0⇒x=π/4+n*π,n∈ℤ

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