If `A = tan 1 and B =tan ^(-1) 1` then

Options

A. `A = B`
B. `A gt B`
C. `A ltB`
D. none of these

Answer

To solve the problem, we need to analyze the values of \( A \) and \( B \) given in the question.

1. **Identify the values of A and B:**
- \( A = \tan(1) \)
- \( B = \tan^{-1}(1) \)

2. **Calculate \( B \):**
- The value of \( \tan^{-1}(1) \) is known to be \( \frac{\pi}{4} \) radians, since \( \tan\left(\frac{\pi}{4}\right) = 1 \).
- Therefore, \( B = \frac{\pi}{4} \).

3. **Calculate \( A \):**
- \( A = \tan(1) \) where 1 is in radians. We will need to find the numerical value of \( \tan(1) \).
- Using a calculator, we find that \( \tan(1) \approx 1.5574 \).

4. **Compare A and B:**
- Now we have \( A \approx 1.5574 \) and \( B = \frac{\pi}{4} \approx 0.7854 \).
- Since \( 1.5574 > 0.7854 \), we conclude that \( A > B \).

5. **Final conclusion:**
- Therefore, the relation between \( A \) and \( B \) is \( A > B \).

### Summary of the Solution:
- \( A = \tan(1) \approx 1.5574 \)
- \( B = \tan^{-1}(1) = \frac{\pi}{4} \approx 0.7854 \)
- Hence, \( A > B \).