Find the value of $tan(cos^(-1)(3/x))$ ?

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Answer 1 · 2017-10-24T17:11:24

$tan(cos^(-1)(3/x))=tant=1/3sqrt(x^2-9)$

Let $cos^(-1)(3/x)=t$

then $cost=3/x$

and therefore $sect=x/3$

and $sec^2x=x^2/9$ and $tan^2t=x^2/9-1=(x^2-9)/9$

and $tant=1/3sqrt(x^2-9)$

hence $tan(cos^(-1)(3/x))=tant=1/3sqrt(x^2-9)$

Find the value of tan(cos^(-1)(3/x))tan(cos^(-1)(3/x))?