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For the principal value, evaluate tan...

For the principal value, evaluate `tan^(-1)(-1)+cos^(-1)(-1/(sqrt(2)))`

A

`pi/2`

B

`pi`

C

`(3pi)/2`

D

`(2pi)/3`

Text Solution

Verified by Experts

The correct Answer is:
A
Range of `tan^(-1)` is `(-pi/2,pi/2)`.
`tan^(-1)(-1)=x rArr tanx=-1=-tanpi/4 = tan(-pi/4) rArr x=-pi/4`.
Range of `cos^(-1)` is `[0,pi]`.
`cos^(-1)(-1/sqrt(2))=y rArr cosy=-1/sqrt(2)=-cospi/4=cos(pi-pi/4)=cos(3pi)/4 rArr y=(3pi)/4`.
`therefore` given exp. `=-pi/4+(3pi)/4=(2pi)/4=pi/2`.
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