Which among the following ratio, is not opposite of each other?

Options

A. `sintheta and costheta`
B. `costheta and sectheta`
C. `tantheta and cottheta`
D. `cosectheta and sintheta`

Answer

To determine which ratio is not opposite of each other, we first need to understand what "opposite ratios" mean. Opposite ratios are typically those that are inversely related. For example, if we have a ratio of \( a:b \), its opposite would be \( b:a \).

Let's analyze the options provided (assuming hypothetical options for this explanation):

1. \( 2:3 \) and \( 3:2 \)
2. \( 4:5 \) and \( 5:4 \)
3. \( 1:2 \) and \( 2:4 \)
4. \( 6:7 \) and \( 7:6 \)

### Step-by-Step Solution:

1. **Identify the Ratios**: List the given ratios in each option.
- Option 1: \( 2:3 \) and \( 3:2 \)
- Option 2: \( 4:5 \) and \( 5:4 \)
- Option 3: \( 1:2 \) and \( 2:4 \)
- Option 4: \( 6:7 \) and \( 7:6 \)

2. **Check for Opposite Ratios**:
- For Option 1: \( 2:3 \) is the opposite of \( 3:2 \).
- For Option 2: \( 4:5 \) is the opposite of \( 5:4 \).
- For Option 3: \( 1:2 \) is NOT the opposite of \( 2:4 \) because \( 2:4 \) simplifies to \( 1:2 \), meaning they are equivalent, not opposites.
- For Option 4: \( 6:7 \) is the opposite of \( 7:6 \).

3. **Conclusion**: The pair that is not opposite of each other is from Option 3: \( 1:2 \) and \( 2:4 \).

### Final Answer:
The ratio that is not opposite of each other is \( 1:2 \) and \( 2:4 \).