Question

Evaluate the following:

`cosec^-1(cosec  (6pi)/5)`

Answer 1

We know that

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

`cosec^-1(cosec  (6pi)/5)=cosec^-1[cosec(pi+pi/5)]`

`=cosec^-1(cosec-pi/5)`

`=-pi/5`