Find the value of
Question:

Find the value of $\cot \left(\tan ^{-1} a+\cot ^{-1} a\right)$

Solution:

$\cot \left(\tan ^{-1} a+\cot ^{-1} a\right)$

$=\cot \left(\frac{\pi}{2}\right) \quad\left[\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right]$

$=0$