Question

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

Answer 1

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

Explanation:

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`