Question

solve the equation for exact solutions over the interval 0,2π).

cot²x + 9 = 0

select the correct answer below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is

b. the solution is the empty set ∅.

Explanation:

Step1: Rearrange the equation

$$\cot^{2}x=- 9$$

Step2: Analyze the range of cotangent function

Since \(\cot^{2}x\geq0\) for all real \(x\) where \(\cot x\) is defined (\(x
eq n\pi,n\in\mathbb{Z}\)), and the right - hand side of the equation \(\cot^{2}x=-9\) is negative.

Answer:

B. The solution is the empty set \(\varnothing\).