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

Answer

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

### Step 1: Use the Pythagorean Identity
We know from the Pythagorean identity that:
\[ \sin^2 A + \cos^2 A = 1 \]
From this, we can express \(\sin^2 A\) as:
\[ \sin^2 A = 1 - \cos^2 A \]

### Step 2: Substitute \(\sin^2 A\) into the expression
Now, we can substitute \(\sin^2 A\) into our expression:
\[ (1 - \cos^2 A) \cdot \csc^2 A = \sin^2 A \cdot \csc^2 A \]

### Step 3: Recall the definition of \(\csc^2 A\)
The cosecant function is defined as:
\[ \csc A = \frac{1}{\sin A} \]
Thus, we have:
\[ \csc^2 A = \frac{1}{\sin^2 A} \]

### Step 4: Substitute \(\csc^2 A\) into the expression
Now, substituting \(\csc^2 A\) into our expression gives:
\[ \sin^2 A \cdot \csc^2 A = \sin^2 A \cdot \frac{1}{\sin^2 A} \]

### Step 5: Simplify the expression
When we multiply \(\sin^2 A\) by \(\frac{1}{\sin^2 A}\), we get:
\[ \sin^2 A \cdot \frac{1}{\sin^2 A} = 1 \]

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