The angle of dip at a place is `delta`. If the dip is measured in a plane makinng an angle `theta` with the magnetic merdian, the apparent angle of dip `delta_(1)` will be

Options

A. `Tan^(-1)(tandelta)`
B. `tan^(-1)(tan delta cos theta)`
C. `tan^(-1)(tan delta sec theta)`
D. `0`

Explanation

To find the apparent angle of dip \( \delta_1 \) when the dip is measured in a plane making an angle \( \theta \) with the magnetic meridian, we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Components of Earth's Magnetic Field**:
The Earth's magnetic field can be resolved into two components:
- The horizontal component \( B_H \)
- The vertical component \( B_V \)

2. **Define the Angle of Dip**:
The angle of dip \( \delta \) is defined as the angle that the resultant magnetic field makes with the horizontal. The tangent of the angle of dip is given by:
\[ \tan(\delta) = \frac{B_V}{B_H} \]

3. **Adjust for the Plane's Orientation**:
When measuring the dip in a plane that is inclined at an angle \( \theta \) to the magnetic meridian, the components of the magnetic field will change. The new horizontal component \( B_{H1} \) and vertical component \( B_{V1} \) can be expressed as:
\[ B_{H1} = B_H \cos(\theta) + B_V \sin(\theta) \]
\[ B_{V1} = B_V \cos(\theta) - B_H \sin(\theta) \]

4. **Calculate the Apparent Angle of Dip**:
The apparent angle of dip \( \delta_1 \) can be calculated using the new components:
\[ \tan(\delta_1) = \frac{B_{V1}}{B_{H1}} \]
Substituting the expressions for \( B_{H1} \) and \( B_{V1} \):
\[ \tan(\delta_1) = \frac{B_V \cos(\theta) - B_H \sin(\theta)}{B_H \cos(\theta) + B_V \sin(\theta)} \]

5. **Final Expression**:
Thus, the apparent angle of dip \( \delta_1 \) can be expressed as:
\[ \delta_1 = \tan^{-1} \left( \frac{B_V \cos(\theta) - B_H \sin(\theta)}{B_H \cos(\theta) + B_V \sin(\theta)} \right) \]