Question

By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:

• A. \( 1.07 \)
• B. \( 0.965 \)
• C. \( 1.035 \)
• D. \( 0.93 \)

Hint:

For small angles, use the approximation \( \cot(45^\circ + \theta) \approx \frac{1 - \theta}{1 + \theta} \) to estimate values efficiently.

Answer 1

The Correct Option is D

Step 1: Using small-angle approximation We use: \[ \cot(45^\circ + \theta) \approx \frac{1 - \theta}{1 + \theta}. \] Substituting \( \theta = 2' = 2 \times 0.0175 \), we compute: \[ \cot 45^\circ 2' \approx \frac{1 - 0.035}{1 + 0.035} = \frac{0.965}{1.035} \approx 0.93. \]