Question:
Find the principal value of each of the following :
$\cot \left(\tan ^{-1} x+\cot ^{-1} x\right)$
Solution:
$\cot \left(\tan ^{-1} x+\cot ^{-1} x\right)=\cot \left(\frac{\pi}{2}\right)\left[\right.$ Formula: $\left.\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right]$
Putting value of $\cot \left(\frac{\pi}{2}\right)$
$=0$
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