Question

Evaluate the following:

`cosec^-1{cosec  (-(9pi)/4)}`

Answer 1

We know that

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

`cosec^-1{cosec  (-(9pi)/4)}=cosec^-1[-cosec(2pi+pi/4)]`

`=cosec^-1(-cosec  pi/4)`

`=cosec^-1(cosec-pi/4)`

`=-pi/4`