Evaluate each of the following:

(i)`cot^(-1)(cot(19pi)/6)`

(ii) `cot^(-1){cot(-(8pi)/3)}`

(iii) `cot^(-1){cot((21pi)/4)}`

Explanation

(i)


We know that
$$ \cot ^{-1}(\cot \theta)=\theta, \quad(0, \pi) $$
We have
$$
...