What is `(sin theta+1)/(cos theta)` equal to?

Options

A. A)`(sin theta+cos theta-1)/(sin theta+cos theta+1)`
B. B)`(sin theta+cos theta+1)/(sin theta+cos theta-1)`
C. C)`(sin theta-cos theta-1)/(sin theta+cos theta+1)`
D. D)`(sin theta-cos theta+1)/(sin theta+cos theta-1)`

Answer

To find the value of \(\frac{\sin \theta + 1}{\cos \theta}\), we can simplify the expression step by step.

### Step-by-Step Solution:

1. **Start with the expression**:
\[ \frac{\sin \theta + 1}{\cos \theta} \]

2. **Separate the fraction**:
We can separate the fraction into two parts:
\[ \frac{\sin \theta}{\cos \theta} + \frac{1}{\cos \theta} \]

3. **Use trigonometric identities**:
Recall that \(\frac{\sin \theta}{\cos \theta} = \tan \theta\) and \(\frac{1}{\cos \theta} = \sec \theta\). Thus, we can rewrite the expression as:
\[ \tan \theta + \sec \theta \]

4. **Final expression**:
Therefore, the expression \(\frac{\sin \theta + 1}{\cos \theta}\) simplifies to:
\[ \tan \theta + \sec \theta \]

### Final Answer:
\[ \frac{\sin \theta + 1}{\cos \theta} = \tan \theta + \sec \theta \]

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