30 answer 

Problem:

If secA tanA = p, find the value of cosecA.

Solution:

We are given that secA tanA = p.

Let's use the trigonometric identities to solve this problem.

Trigonometric identities:
- secA = 1/cosA
- tanA = sinA/cosA
- cosecA = 1/sinA

Using the given information:
We have secA tanA = p.

Substituting the values from the trigonometric identities, we can rewrite the equation as:

(1/cosA) * (sinA/cosA) = p

Simplifying the equation further, we get:

sinA/cos^2A = p

Now, we can cross-multiply to eliminate the fractions:

sinA = p * cos^2A

Solving for cosecA:
We know that cosecA = 1/sinA.

Taking the reciprocal of both sides of the equation sinA = p * cos^2A, we get:

1/sinA = 1/(p * cos^2A)

Now, substituting cosecA in place of 1/sinA, we have:

cosecA = 1/(p * cos^2A)

Therefore, the value of cosecA is 1/(p * cos^2A).

Conclusion:
The value of cosecA is 1/(p * cos^2A).