Question

Evaluate the following:

`sec^-1(sec  (5pi)/4)`

Answer 1

We know that

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

 We have 

`sec^-1(sec  (5pi)/4)=sec^-1[sec(2pi-(3pi)/4)]`

`=sec^-1[sec((3pi)/4)]`

`=(3pi)/4`