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

Answer

To solve the expression \( (1 - \cos^2 A) \cdot \csc^2 A \), 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 \( 1 - \cos^2 A \) as:
\[ 1 - \cos^2 A = \sin^2 A \]

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

### Step 3: Recall the Definition of Cosecant
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 Cosecant into the Expression
Now we can substitute \( \csc^2 A \) into our expression:
\[ \sin^2 A \cdot \csc^2 A = \sin^2 A \cdot \frac{1}{\sin^2 A} \]

### Step 5: Simplify the Expression
When we simplify this, we find:
\[ \sin^2 A \cdot \frac{1}{\sin^2 A} = 1 \]

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