**Proof:**

To prove that SinA/(secA tanA-1) CosA/(cosecA cotA-1) = 1, we need to simplify the expression on the left side of the equation and show that it equals 1.

Let's start by simplifying the expression step by step:

1. Rewrite secA, tanA, cosecA, and cotA in terms of sine and cosine:

- secA = 1/cosA
- tanA = sinA/cosA
- cosecA = 1/sinA
- cotA = cosA/sinA

Substituting these values into the expression, we have:

SinA/(1/cosA * sinA/cosA - 1) * CosA/(1/sinA * cosA/sinA - 1)

2. Simplify the denominators:

- (1/cosA * sinA/cosA - 1) = (sinA - cosA) / cos^2A
- (1/sinA * cosA/sinA - 1) = (cosA - sinA) / sin^2A

Substituting these values back into the expression, we have:

SinA/(sinA - cosA)/cos^2A * CosA/(cosA - sinA)/sin^2A

3. Simplify the expression further:

- Invert the second fraction and multiply:

SinA/(sinA - cosA)/cos^2A * sin^2A/(cosA - sinA)

- Cancel out common factors:

SinA * sin^2A / (sinA - cosA) * cos^2A / (cosA - sinA)

- Rearrange the terms:

sin^3A * cos^2A / ((sinA - cosA) * (cosA - sinA))

- Notice that (sinA - cosA) and (cosA - sinA) are negative of each other:

sin^3A * cos^2A / (-(sinA - cosA) * (sinA - cosA))

- Simplify the expression:

sin^3A * cos^2A / (sinA - cosA)^2

4. Apply the identity sin^2A + cos^2A = 1:

sin^3A * cos^2A / (sinA - cosA)^2 = sin^3A * cos^2A / (1 - 2sinAcosA + cos^2A)

5. Cancel out common factors:

sin^3A / (1 - 2sinAcosA + cos^2A)

6. Apply the identity sinA * sinA * sinA = sin^3A:

sinA * sinA * sinA / (1 - 2sinAcosA + cos^2A)

7. Apply the identity sinA * cosA = 1/2 * sin(2A):

sinA * sinA * sinA / (1 - sin(2A) + cos^2A)

8. Apply the identity 1 - sin(2A) = cos^2A:

sinA * sinA * sinA / cos^2