Question

The approximate value of \( \cot^{-1} (1 \cdot 001) \) is

• A. \( \frac{\pi}{4} - 0 \cdot 0005 \)
• B. \( \frac{\pi}{4} + 0 \cdot 005 \)
• C. \( \frac{\pi}{4} - 0 \cdot 0005 \)
• D. \( \frac{\pi}{4} - 0 \cdot 005 \)

Hint:

For small angle approximations, \( \cot^{-1}(1 + x) \approx \frac{\pi}{4} - x \).

Answer 1

The Correct Option is A

Step 1: Approximation using small angle.
Since \( 1 \cdot 001 \) is close to 1, we can use the approximation for small values of \( x \), where \( \cot^{-1} (1 + x) \approx \frac{\pi}{4} - x \). In this case, the value of \( x = 0 \cdot 0005 \).
Step 2: Conclusion.
Thus, the approximate value is \( \frac{\pi}{4} - 0 \cdot 0005 \), corresponding to option (A).