If `theta_1` and `theta_2` be the apparent angles of dip observed in two vertical planes at right angles to each other, then show that the true angle of dip, `theta` is given by `cot^2theta=cot^2theta+cot^2theta`.

Explanation

To derive the expression for the true angle of dip \( \theta \) in terms of the apparent angles of dip \( \theta_1 \) and \( \theta_2 \), we start with the definitions and relationships involving the angles of dip.

### Step 1: Understanding the Angles of Dip
The angle of dip \( \theta \) is defined as the angle between the Earth's magnetic field and the horizontal plane. When observed from two vertical planes at right angles to each other, we denote the angles of dip as \( \theta_1 \) and \( \theta_2 \).

### Step 2: Establishing Relationships
From the geometry of the situation, we can express the horizontal and vertical components of the magnetic field. The vertical component \( V \) can be expressed in terms of the angles of dip:

...