How do you simplify $Cos[tan^-1(-1)]$ ?

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Answer 1 · 2016-06-26T11:40:29

$1/sqrt 2$ , for the principal value $-pi/4$ of $tan^(-1)(-1)$ .
Against , $(3pi)/4$ , the answer is $-1/sqrt 2$ .

If $a = tan^(-1)(-1), tan a = -1.$ ,

a is in either 4th quadrant with the principal value $-pi/4$ or in

the 2nd, as $(3pi)/4$ .

So, the given cosine cos a is

$cos (-pi/4)=1/sqrt 2$ or

$cos((3pi)/4)=cos (pi-pi/4)=-cos(pi/4)=-1/sqrt 2$ .

In brief, the answer is $+-1/sqrt 2$ for the general value of $tan^(-1)(-1)$ ..

How do you simplify Cos[tan^-1(-1)]Cos[tan^-1(-1)]?