Solve for x 2cot(x)+1=-1

Problem

2*cot(x)+1=−1

Solution

1. Isolate the cotangent term by subtracting 1 from both sides of the equation.

2*cot(x)=−2

2. Divide both sides by 2 to solve for cot(x)

cot(x)=−1

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

tan(x)=−1

4. Identify the reference angle where tan(θ)=1 which is π/4 Since the tangent value is negative, the angle must be in the second or fourth quadrant.

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

x=(3*π)/4+n*π

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