Evaluate each of the following:

(i)`tan^(-1)(tan4)`

(ii) `tan^(-1)(tan12)`

Explanation

(i) We know that,


`\tan ^{-1}(\tan \theta)=\theta, \quad\left[-\frac{\pi}{2}<\theta<\frac{\pi}{2}\right]`


We have


`\Rightarrow \tan ^{-1}(\tan 4)=& \tan ^{-1}[\tan (-\pi+4)]`

`=-\pi+4`

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