Question

How do you find the value for `csc (Tan^-1 (4/5))`?

Answer 1

`sqrt41/4`

Explanation:

let`tan^(-1)(4/5)=theta`
`tantheta=4/5`
`cottheta=5/4`
`1+cot^2theta=1+25/16=41/16`
`cosec^2theta=41/16`
`theta=csc^(-1)sqrt(41/16)`
`csctheta=csccsc^(-1)sqrt(41/16)=sqrt(41/16)=sqrt41/4`