How do you find the exact value of $sec(arctan(12/5))$ ?

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Answer 1 · 2017-05-11T06:03:30

$sec(arctan(12/5))=13/5$

Let $arctan(12/5)=alpha$

then $tanalpha=12/5$

and hence $secalpha=sqrt(1+tan^2alpha)$

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

= $sqrt(169/25)=13/5$

Hence $sec(arctan(12/5))=13/5$

How do you find the exact value of sec(arctan(12/5))sec(arctan(12/5))?