If `alpha, beta , gamma` are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction-cosines of the line are :

Options

A. `lt "sin " alpha, sin beta, sin gamma gt`
B. `lt cos alpha, cos beta, cos gamma gt`
C. `lt tan alpha, tan beta , tan gamma gt `
D. `lt cos^(2) alpha, cos^(2) beta, cos^(2) gamma gt `.

Answer

To find the direction cosines of a line that makes angles α, β, and γ with the positive directions of the x, y, and z axes respectively, we can follow these steps:

### Step-by-step Solution:

1. **Understanding Direction Cosines**:
- The direction cosines of a line are defined as the cosines of the angles that the line makes with the coordinate axes.

2. **Identify the Angles**:
- Let α be the angle between the line and the positive x-axis.
- Let β be the angle between the line and the positive y-axis.
- Let γ be the angle between the line and the positive z-axis.

3. **Calculate the Direction Cosines**:
- The direction cosine with respect to the x-axis is given by:
\[ l = \cos \alpha \]
- The direction cosine with respect to the y-axis is given by:
\[ m = \cos \beta \]
- The direction cosine with respect to the z-axis is given by:
\[ n = \cos \gamma \]

4. **Final Representation**:
- Therefore, the direction cosines of the line can be represented as:
\[ (l, m, n) = (\cos \alpha, \cos \beta, \cos \gamma) \]

### Conclusion:
The direction cosines of the line are \( \cos \alpha, \cos \beta, \cos \gamma \).