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Question
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
Solution
`tan^-1(-1)+cos^-1(-1/sqrt2)`
`=tan^-1{tan(-pi/4)}+cos^-1(cos (3pi)/4)` `[because "Range of tan is" (-pi/2,pi/2) ; -pi/4 in(-pi/2,pi/2) "and range of cosine is"[0,pi] ; (3pi)/4 in [0, pi]]`
`=-pi/4+(3pi)/4`
`=pi/2`
`therefore tan^-1(-1)+cos^-1(-1/sqrt2)=pi/2`
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