The expression
`cosec^(2)A cot^(2)A-sec^(2)A tan^(2)A-(cot^(2)A-tan^(2)A)(sec^(2)A cosec^(2)A-1)` is equal to

Options

A. 1
B. `-1`
C. 0
D. 2

Answer

To solve the expression \( \csc^2 A \cot^2 A - \sec^2 A \tan^2 A - (\cot^2 A - \tan^2 A)(\sec^2 A \csc^2 A - 1) \), we will simplify it step by step.

### Step 1: Rewrite the expression
We start with the given expression:
\[ \csc^2 A \cot^2 A - \sec^2 A \tan^2 A - (\cot^2 A - \tan^2 A)(\sec^2 A \csc^2 A - 1) \]

### Step 2: Expand the second part
Now, let's expand the second part of the expression:
\[ (\cot^2 A - \tan^2 A)(\sec^2 A \csc^2 A - 1) \]
Using the identity \( \sec^2 A = 1 + \tan^2 A \) and \( \csc^2 A = 1 + \cot^2 A \), we can rewrite this as:
\[ (\cot^2 A - \tan^2 A)((1 + \tan^2 A)(1 + \cot^2 A) - 1) \]
This simplifies to:
\[ (\cot^2 A - \tan^2 A)(\tan^2 A \cot^2 A + \tan^2 A + \cot^2 A) \]

### Step 3: Substitute identities
Next, we will use the identities:
\[ \cot^2 A = \frac{1}{\tan^2 A} \]
and simplify the expression:
\[ \cot^2 A - \tan^2 A = \frac{1 - \tan^4 A}{\tan^2 A} \]
Thus, we can rewrite the expression as:
\[ \csc^2 A \cot^2 A - \sec^2 A \tan^2 A - \left(\frac{1 - \tan^4 A}{\tan^2 A}\right)(\tan^2 A \cot^2 A + \tan^2 A + \cot^2 A) \]

### Step 4: Combine like terms
Now, we will combine the terms:
\[ \csc^2 A \cot^2 A - \sec^2 A \tan^2 A - \left(\frac{(1 - \tan^4 A)(\tan^2 A \cot^2 A + \tan^2 A + \cot^2 A)}{\tan^2 A}\right) \]
This can be quite complex, but we can notice that many terms will cancel out.

### Step 5: Final simplification
After simplifying and canceling out terms, we find that the expression simplifies to:
\[ 0 \]

### Conclusion
Thus, the final value of the expression is:
\[ \boxed{0} \]