Evaluate each of the following:

(i)`tan^(-1)(tan((9pi)/4))`

(ii) `tan^(-1)(tan1)`

(iii) `tan^(-1)(tan2)`

Explanation

(i) Given as `\tan ^{-1}(\tan ((9pi) / 4)`

As we know that `\tan( (9 pi) / 4)=1`

On, substituting this value in `\tan ^{-1}(\tan(( 9pi )/ 4))` we get,

`\tan ^{-1}(1)`

Let `\tan ^{-1}(1)=y`

`\tan y=1`

`\tan (\pi / 4)=1`

So, the range of the principal value of` \tan ^{-1} is (-\pi / 2, \pi / 2) and \tan (\pi / 4)=1`

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