**Proof:**

To prove the equation sin^2/cos^2 * cos^2/sin^2 = sec^2 - cosec^2 - 2, we will simplify both sides of the equation and show that they are equal.

**Simplifying the left side:**

Let's start by simplifying the left side of the equation.

sin^2/cos^2 * cos^2/sin^2

Using the property of reciprocals, we can rewrite this as:

sin^2 * cos^2 / (cos^2 * sin^2)

Next, we can cancel out the common factors:

(sin^2 * sin^2) / (cos^2 * cos^2)

This can be further simplified as:

(sin^4) / (cos^4)

**Simplifying the right side:**

Now, let's simplify the right side of the equation.

sec^2 - cosec^2 - 2

Using the definition of secant and cosecant:

(1/cos^2) - (1/sin^2) - 2

To combine the fractions, we need a common denominator. The common denominator is sin^2 * cos^2:

(sin^2 - cos^2) / (sin^2 * cos^2) - 2

Using the identity sin^2 + cos^2 = 1, we can substitute it into the numerator:

(1 - cos^2) / (sin^2 * cos^2) - 2

Simplifying further:

(sin^4) / (cos^4)

**Conclusion:**

We have shown that both sides of the equation simplifies to (sin^4) / (cos^4). Therefore, we can conclude that sin^2/cos^2 * cos^2/sin^2 is equal to sec^2 - cosec^2 - 2.