Question

Evaluate the following:

`cosec^-1(cosec  (11pi)/6)`

Answer 1

We know that

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

`cosec^-1(cosec  (11pi)/6)=cosec^-1[cosec(2pi-pi/6)]`

`=cosec^-1(cosec - pi/6)`

`=-pi/6`