`9 sec^(2) A - 9 tan^(2) A` =

Options

A. 0
B. 3
C. -9
D. 9

Answer

To solve the expression \(9 \sec^2 A - 9 \tan^2 A\), we can follow these steps:

### Step-by-Step Solution:

1. **Factor out the common term:**
\[ 9 \sec^2 A - 9 \tan^2 A = 9 (\sec^2 A - \tan^2 A) \]

2. **Use the trigonometric identity:**
We know the identity:
\[ \sec^2 A - \tan^2 A = 1 \]
Therefore, we can substitute this identity into our expression:
\[ 9 (\sec^2 A - \tan^2 A) = 9 \cdot 1 \]

3. **Simplify the expression:**
\[ 9 \cdot 1 = 9 \]

### Final Answer:
\[ 9 \sec^2 A - 9 \tan^2 A = 9 \]

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