Question

Evaluate the following:

`sec^-1(sec  (9pi)/5)`

Answer 1

We know that

sec^-1 (sec θ) = θ,    [0, π/2) ∪ (π/2, π]

 We have 

`sec^-1(sec  (9pi)/5)=sec^-1[sec(2pi-pi/5)]`

`=sec^-1[sec(pi/5)]`

`=pi/5`