Find the value of `sin^(2)theta*sec^(2)theta`.

Answer

To find the value of \( \sin^2 \theta \cdot \sec^2 \theta \), we can follow these steps:

### Step 1: Write the expression using the definition of secant
We know that:
\[ \sec \theta = \frac{1}{\cos \theta} \]
Thus, we can write:
\[ \sec^2 \theta = \frac{1}{\cos^2 \theta} \]

### Step 2: Substitute secant into the expression
Now, substituting \( \sec^2 \theta \) into the original expression gives us:
\[ \sin^2 \theta \cdot \sec^2 \theta = \sin^2 \theta \cdot \frac{1}{\cos^2 \theta} \]

### Step 3: Simplify the expression
This can be rewritten as:
\[ \sin^2 \theta \cdot \sec^2 \theta = \frac{\sin^2 \theta}{\cos^2 \theta} \]

### Step 4: Recognize the relationship with tangent
We know that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \]
Thus, we can express our equation as:
\[ \frac{\sin^2 \theta}{\cos^2 \theta} = \tan^2 \theta \]

### Conclusion
Therefore, we conclude that:
\[ \sin^2 \theta \cdot \sec^2 \theta = \tan^2 \theta \]