Find the principal value of: `cose c^(-1)(-sqrt(2))`

Explanation

Here the basic trigonometric function of `Sin θ = y`, can be changed to `θ = sin^-1( y)`

Let,

`cosec^- 1 (- sqrt2) = y`

Hence,
`cosec y = -sqrt2`

= `- cosec (pi /4)`

= `cosec (- pi / 4)`

Range of the principal value of `cosec^- 1 (x)`
= `[- pi/2, pi/2] - {0}`
Thus,

principal value of `cosec^-1 (- sqrt2)`
= `(- pi/4)`