Question

Find the principal value of cosec^–1(– 1)

Answer 1

Let y = cosec^–1(– 1)

Where `- pi/2 ≤ y ≤ pi/2`

cosec y = – 1

`1/("cosec" y) = 1/(-1)`

⇒ sin y =  – 1

= `sin (- pi/2)`

⇒ y = `- pi/2`

∴ The principal value of cosec^–1(– 1) =  `- pi/2`