Given:
A B = 90°
sec A = 5/3

To Find:
Value of cosec B

Solution:

Step 1: Understanding the Given Information

In the given problem statement, we are given two pieces of information:
1. The sum of angles A and B is 90 degrees.
2. The secant of angle A is equal to 5/3.

Step 2: Understanding the Concepts

Before solving the problem, let's revise the concepts of trigonometric functions and their reciprocal functions.

1. Secant (sec) function:
The secant of an angle is the reciprocal of the cosine of that angle.
Mathematically, sec A = 1/cos A

2. Cosecant (cosec) function:
The cosecant of an angle is the reciprocal of the sine of that angle.
Mathematically, cosec A = 1/sin A

Step 3: Solving the Problem

From the given information, we know that A + B = 90°.
Since A and B are complementary angles, the sine of A is equal to the cosine of B.
Therefore, sin A = cos B

Using the identity sin^2 A + cos^2 A = 1, we can find the value of sin A:
sin^2 A + cos^2 A = 1
sin^2 A + (1 - sin^2 A) = 1
sin^2 A + 1 - sin^2 A = 1
1 = 1

Since sin A = cos B, we can substitute sin A with cos B in the given equation:
sin A = cos B
1 = cos B

Now, we need to find the value of cosec B.
Using the definition of cosecant, we have:
cosec B = 1/sin B

Since sin B = cos B (as shown above), we can substitute sin B with cos B in the above equation:
cosec B = 1/cos B

Step 4: Applying the Given Information

From the given information, we know that sec A = 5/3.
Using the definition of secant, we have:
sec A = 1/cos A

Substituting the given value of sec A into the equation, we get:
5/3 = 1/cos A

Solving for cos A, we find:
cos A = 3/5

Step 5: Finding the Value of cosec B

Now, we can substitute the value of cos A into the equation for cosec B:
cosec B = 1/cos B
cosec B = 1/(3/5)
cosec B = 5/3

Step 6: Final Answer

Therefore, the value of cosec B is 5/3.