Problem
Evaluate: \( \cot\left(\tan^{-1}(a) + \cot^{-1}(a)\right) \)
Solution
Use identity:
\[ \tan^{-1}(a) + \cot^{-1}(a) = \frac{\pi}{2} \]
Therefore:
\[ \cot\left(\tan^{-1}(a) + \cot^{-1}(a)\right) = \cot\left(\frac{\pi}{2}\right) \]
\[ = 0 \]
Final Answer
\[ \boxed{0} \]
Explanation
The sum of tan⁻¹(a) and cot⁻¹(a) is always π/2, so cot(π/2) = 0.