Solution:

To express the trigonometric ratios sin A, sec A, and tan A in terms of cot A, we need to understand the relationships between these trigonometric functions.

Trigonometric Ratios:
Trigonometric ratios are ratios of the sides of a right triangle. They are defined as follows:

- Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
- Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
- Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.
- Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.
- Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.
- Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.

Relationships:
Using the definitions of these trigonometric ratios, we can establish the following relationships:

- Sine and Cosecant: sin A = 1/csc A
- Cosine and Secant: cos A = 1/sec A
- Tangent and Cotangent: tan A = 1/cot A

Therefore, to express sin A, sec A, and tan A in terms of cot A, we can substitute the reciprocal values into the equations:

- Sine: sin A = 1/csc A = 1/(1/sin A) = sin A
- Secant: sec A = 1/cos A = 1/(1/sec A) = cos A
- Tangent: tan A = 1/cot A = 1/(1/tan A) = tan A

Hence, sin A, sec A, and tan A can be expressed in terms of cot A as sin A, sec A, and tan A respectively.

Summary:
In summary, the trigonometric ratios sin A, sec A, and tan A can be expressed in terms of cot A as sin A, sec A, and tan A respectively. This is done by substituting the reciprocal values of csc A, cos A, and cot A into the equations.