Find the principal values of the following:

    6. \tan^{-1}(-1)

Answers (1)

Given \tan^{-1}(-1) so we can assume it to be equal to 'z';

\tan^{-1}(-1) =z  , 

\tan z = -1     

or        

-\tan (\frac{\pi}{4}) = \tan(\frac{-\pi}{4})= -1                                                 

 And as we know the range of principal values of \tan^{-1} from \left ( \frac{-\pi}{2}, \frac{\pi}{2} \right ).

As only one value z = -\frac{\pi}{4} lies hence we have only one principal value that is -\frac{\pi}{4}.

 

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