Uncategorized: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

If planes are at angles $\alpha$ and $90^{\circ} - \alpha$ with the magnetic meridian, then $\tan \theta_1 = \frac{\tan \theta}{\cos \alpha}$ and $\tan \theta_2 = \frac{\tan \theta}{\sin \alpha}$.
Squaring and adding their inverses gives $\cot^2 \theta_1 + \cot^2 \theta_2 = \frac{\cos^2 \alpha + \sin^2 \alpha}{\tan^2 \theta} = \cot^2 \theta$.