Question

How do you find the exact value of `cos(tan^-1(-1))`?

Answer 1

`cos(tan^(-1)(-1))=1/sqrt2`

Explanation:

`tan^(-1)(-1)` means an angle whose tangent ratio is `-1`.

The range of such an angle is `[-pi/2,pi/2]` and in this range, we have `tan(-pi/4)=-1`.

Hence `tan^(-1)(-1)=-pi/4`

and `cos(tan^(-1)(-1))=cos(-pi/4)=1/sqrt2`