Direction cosines are the cosines of the angles that a given line makes with the positive x, y, and z-axes. They are used to determine the orientation and direction of a line or vector in three-dimensional space.

Direction cosines are denoted by l, m, and n, and they correspond to the cosines of the angles made by the line with the x, y, and z-axes respectively.

The direction cosines can be calculated using the following formulas:

l = cos(α)
m = cos(β)
n = cos(γ)

where α, β, and γ are the angles made by the line with the x, y, and z-axes respectively.

Explanation of Option A:
The option A states that direction cosines are cosines of direction angles, which is correct. The direction cosines are indeed the cosines of the angles made by a line with the x, y, and z-axes.

Explanation of Option B:
The option B states that direction cosines are cotangents of direction angles, which is incorrect. Direction cosines are not cotangents of the direction angles. They are specifically defined as the cosines of the direction angles.

Explanation of Option C:
The option C states that direction cosines are tangents of direction angles, which is incorrect. Direction cosines are not tangents of the direction angles. They are specifically defined as the cosines of the direction angles.

Explanation of Option D:
The option D states that direction cosines are sines of direction angles, which is incorrect. Direction cosines are not sines of the direction angles. They are specifically defined as the cosines of the direction angles.

In conclusion, the correct option is A, which states that direction cosines are the cosines of direction angles. They provide a way to express the orientation and direction of a line or vector in three-dimensional space.