Evaluate each of the following:

(i)`tan^(-1)(tanpi/3)`

(ii) `tan^(-1)(tan(6pi)/7)`

(iii) `tan^(-1)(tan(7pi)/6)`

Explanation

(i) As `\tan ^{-1}(\tan x)=x if x \in[-\pi / 2, \pi / 2]`

On, applying this condition in the given question we get,

`\tan ^{-1}(\tan \pi / 3)=\pi / 3`




(ii) As we know that `\tan 6 \pi / 7` can be written as `(\pi-\pi / 7)`

`\tan (\pi-\pi / 7)=-\tan \pi / 7`




(iii) As we know that `\tan ^{-1}(\tan x)=x if x \in[-\pi / 2, \pi / 2]`

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