Solve for x cot(x)+1=0

Problem

cot(x)+1=0

Solution

1. Isolate the cotangent function by subtracting 1 from 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. Identify the reference angle by finding the value of x where tan(x)=1 in the first quadrant.

(x_ref)=π/4

4. Determine the quadrants where the tangent function is negative, which are Quadrant II and Quadrant IV.

x=π−π/4=(3*π)/4

x=2*π−π/4=(7*π)/4

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

x=(3*π)/4+n*π

Final Answer

cot(x)+1=0⇒x=(3*π)/4+n*π

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