Question

How do you solve and find the value of `cos(arctan(3/5))`?

Answer 1

`cos(arctan(3/5))=5/sqrt34`

Explanation:

Let `arctan(3/5)=theta`

Hence `tantheta=3/5`

and `cos(arctan(3/5))=costheta`

= `1/sectheta`

= `1/sqrt(sec^2theta)`

= `1/sqrt(1+tan^2theta)`

= `1/sqrt(1+(3/5)^2)`

= `1/sqrt(1+9/25)`

= `1/sqrt(34/25)`

= `sqrt(25/34)`

= `5/sqrt34`