Question

​Find the principal value of the following:

cosec^-1(-2)

Answer 1

Let cosec^-1(-2) = y

Then,

cosec y = -2

We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}.`

Thus,

cosec y = -2 = `cosec(-pi/6)`

`y=-pi/6in[-pi/2,pi/2],y!=0`

Hence, the principal value of `cosec^-1(-2)    is  -pi/6`