How do you evaluate $cos[arctan(-5/12)]$ ?

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Answer 1 · 2016-03-03T04:58:29

$cos[arctan(-5/12)]=+-12/13$

$arctan(-5/12)$ means an angle $theta$ whose $tantheta=-5/12$ . As such we have to find $costheta$ .

$costheta=1/sectheta=sqrt(1/sec^2theta)=sqrt(1/(1+tan^2theta))$

Hence

$costheta=sqrt(1/(1+(-5/12)^2))=sqrt(1/(1+25/144))$

= $sqrt(1/(169/144))=sqrt(144/169)=+-12/13$

Hence $cos[arctan(-5/12)]=+-12/13$

How do you evaluate cos[arctan(-5/12)]cos[arctan(-5/12)]?