Question

Find the principal value of the following:

cosec^-1 (2)

Answer 1

Let cosec^-1 (2) = y

2 = cosec y

(or) cosec y = 2

`=> 1/(sin y) = 2`

`=> sin y = 1/2`  (Take reciprocal)

⇒ sin y = sin `(pi/6)`

⇒ sin y = `pi/6`

The principal value of cosec^-1 (-1) is `pi/6`.