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

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Answer 1 · 2016-12-28T14:19:43

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

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

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