Question Solve the trigonometric equation $\cot^2 x + 12 \cot x = 0$ for $x$.

Studdy Solution
Combine the solutions from steps 9 and 14 to get the complete set of solutions for the original equation.
$$x = \frac{\pi}{2} + k\pi, \quad k \in \mathbb{Z}$$ $$x = \arctan\left(-\frac{1}{12}\right) + k\pi, \quad k \in \mathbb{Z}$$
These are the values of $x$ that satisfy the equation $\cot^2 x + 12 \cot x = 0$.