Solve for x square root of 3cot(x)+1=0

Problem

√(,3)*cot(x)+1=0

Solution

1. Isolate the term containing the trigonometric function by subtracting 1 from both sides of the equation.

√(,3)*cot(x)=−1

2. Divide both sides by √(,3) to solve for cot(x)

cot(x)=−1/√(,3)

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

tan(x)=−√(,3)

4. Identify the reference angle where tan(θ)=√(,3) which is π/3 (or 60.

5. Determine the angles in the interval [0,2*π) where the tangent function is negative (Quadrants II and IV).

x=π−π/3=(2*π)/3

x=2*π−π/3=(5*π)/3

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

x=(2*π)/3+n*π

Final Answer

√(,3)*cot(x)+1=0⇒x=(2*π)/3+n*π

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