What is \tan^{-1}\cot(\text{cosec}^{-1}2) equal to ?
- A. \frac{\pi}{8}
- B. \frac{\pi}{6}
- C. \frac{\pi}{4}
- D. \frac{\pi}{3} ✓
Correct Answer: D. \frac{\pi}{3}
Explanation
First, evaluate the innermost part: \text{cosec}^{-1}(2) = \frac{\pi}{6}. Next, substitute this back in to get \cot(\frac{\pi}{6}) = \sqrt{3}. Finally, \tan^{-1}(\sqrt{3}) = \frac{\pi}{3}.