Introduction:
In trigonometry, there are six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent. These ratios are defined based on the sides of a right-angled triangle. In this case, we will be discussing the other trigonometric ratios of angle A in terms of cosecA.

Trigonometric Ratios:
1. Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted by sin(A). Therefore, sin(A) = 1/cosec(A).

2. Cosine (cos): The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is denoted by cos(A). Using the reciprocal identity, we can express it in terms of cosec(A) as cos(A) = 1/sin(A) = 1/(1/cosec(A)) = cosec(A).

3. Tangent (tan): The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is denoted by tan(A). Using the reciprocal identity, we can express it in terms of cosec(A) as tan(A) = sin(A)/cos(A) = (1/cosec(A))/cosec(A) = 1/cosec^2(A).

4. Secant (sec): The secant of an angle is defined as the reciprocal of the cosine of that angle. It is denoted by sec(A). Using the reciprocal identity, we can express it in terms of cosec(A) as sec(A) = 1/cos(A) = 1/cosec(A).

5. Cosecant (cosec): The cosecant of an angle is defined as the reciprocal of the sine of that angle. It is denoted by cosec(A). Therefore, cosec(A) = 1/sin(A) = 1/(1/cosec(A)) = cosec(A).

6. Cotangent (cot): The cotangent of an angle is defined as the reciprocal of the tangent of that angle. It is denoted by cot(A). Using the reciprocal identity, we can express it in terms of cosec(A) as cot(A) = 1/tan(A) = 1/(1/cosec^2(A)) = cosec^2(A).

Summary:
- sin(A) = 1/cosec(A)
- cos(A) = cosec(A)
- tan(A) = 1/cosec^2(A)
- sec(A) = 1/cosec(A)
- cosec(A) = cosec(A)
- cot(A) = cosec^2(A)

These trigonometric ratios are useful in solving various trigonometric problems and applications.