Find the value of `("cosec"^(2)A-1)*tan^(2)A`.

Answer

To find the value of \((\csc^2 A - 1) \cdot \tan^2 A\), we can follow these steps:

### Step 1: Use the identity for \(\csc^2 A\)
We know that:
\[ \csc^2 A = 1 + \cot^2 A \]
Thus, we can rewrite \(\csc^2 A - 1\) as:
\[ \csc^2 A - 1 = \cot^2 A \]

### Step 2: Substitute \(\tan^2 A\) in terms of \(\sin A\) and \(\cos A\)
We know that:
\[ \tan A = \frac{\sin A}{\cos A} \]
Therefore,
\[ \tan^2 A = \frac{\sin^2 A}{\cos^2 A} \]

### Step 3: Substitute into the original expression
Now, substituting the values we have:
\[ (\csc^2 A - 1) \cdot \tan^2 A = \cot^2 A \cdot \tan^2 A \]

### Step 4: Express \(\cot^2 A\) in terms of \(\tan^2 A\)
We know that:
\[ \cot A = \frac{1}{\tan A} \]
Thus,
\[ \cot^2 A = \frac{1}{\tan^2 A} \]

### Step 5: Substitute \(\cot^2 A\) into the expression
Now substituting \(\cot^2 A\):
\[ \cot^2 A \cdot \tan^2 A = \frac{1}{\tan^2 A} \cdot \tan^2 A \]

### Step 6: Simplify the expression
This simplifies to:
\[ \frac{\tan^2 A}{\tan^2 A} = 1 \]

### Final Answer
Thus, the value of \((\csc^2 A - 1) \cdot \tan^2 A\) is:
\[ \boxed{1} \]