How do you evaluate $tan(cos^-1((-1/sqrt2)))$ without a calculator?

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Answer 1 · 2017-02-03T14:10:59

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

From the definition of $cos^(-1)$ , if $costheta=x$ , then $cos^(-1)x=theta$ , but within range $[0,pi]$

As $cos((3pi)/4)=-1/sqrt2$ ,

$cos^(-1)(-1/sqrt2)=(3pi)/4$

Hence $tan(cos^(-1)(-1/sqrt2))=tan((3pi)/4)=-1$

How do you evaluate tan(cos^-1((-1/sqrt2)))tan(cos^-1((-1/sqrt2))) without a calculator?