Solve: `1+ tan^(2) theta =` ? A. `cos^(2) theta`
B. `sec^(2) theta`
C. `tan^(2) theta`
D. 2

Options

A. A
B. C
C. D
D. B

Answer

To solve the equation \( 1 + \tan^2 \theta = ? \), we can use a fundamental trigonometric identity.

### Step-by-Step Solution:

1. **Recall the Trigonometric Identity**:
The identity we will use is:
\[ 1 + \tan^2 \theta = \sec^2 \theta \]

2. **Substituting the Identity**:
From the identity, we can directly substitute:
\[ 1 + \tan^2 \theta = \sec^2 \theta \]

3. **Conclusion**:
Therefore, the solution to the equation \( 1 + \tan^2 \theta \) is:
\[ \sec^2 \theta \]

### Final Answer:
The correct option is **B. \( \sec^2 \theta \)**.