`cos theta . Sec theta =`

Options

A. 0
B. `(1)/(2) `
C. 1
D. `sqrt(2)`

Answer

To solve the expression \( \cos \theta \cdot \sec \theta \), we will use the definitions of cosine and secant in trigonometry.

### Step-by-Step Solution:

1. **Recall the definitions**:
- The cosine of an angle \( \theta \) is defined as:
\[ \cos \theta = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{B}{H} \]
- The secant of an angle \( \theta \) is defined as:
\[ \sec \theta = \frac{\text{Hypotenuse}}{\text{Adjacent side}} = \frac{H}{B} \]

2. **Substitute the definitions into the expression**:
- Now, substituting these definitions into the expression \( \cos \theta \cdot \sec \theta \):
\[ \cos \theta \cdot \sec \theta = \left(\frac{B}{H}\right) \cdot \left(\frac{H}{B}\right) \]

3. **Multiply the fractions**:
- When we multiply these fractions, we get:
\[ \cos \theta \cdot \sec \theta = \frac{B \cdot H}{H \cdot B} \]

4. **Simplify the expression**:
- The \( B \) in the numerator and denominator cancels out, as does the \( H \):
\[ \frac{B \cdot H}{H \cdot B} = \frac{1}{1} = 1 \]

5. **Final result**:
- Therefore, the final result is:
\[ \cos \theta \cdot \sec \theta = 1 \]