Find in the blank.
`tan^(2)theta=.......-1`.

Options

A. `cot^(2)theta`
B. `sec^(2)theta`
C. `"cosec"^(2)theta`
D. `cos^(2)theta`

Answer

To solve the equation \( \tan^2 \theta = \ldots - 1 \), we can use the trigonometric identity that relates tangent and secant.

### Step-by-Step Solution:

1. **Recall the Identity**:
We know the trigonometric identity:
\[ \sec^2 \theta = 1 + \tan^2 \theta \]

2. **Rearranging the Identity**:
From the identity, we can rearrange it to express \( \tan^2 \theta \):
\[ \tan^2 \theta = \sec^2 \theta - 1 \]

3. **Fill in the Blank**:
Thus, we can fill in the blank in the original equation:
\[ \tan^2 \theta = \sec^2 \theta - 1 \]

4. **Final Answer**:
Therefore, the answer to the question is:
\[ \tan^2 \theta = \sec^2 \theta - 1 \]