If and y = sin^–1 (sin x), find

For ,

y=sin^-1 (sin x)

= sin^-1 ( sin (π –(π -x))

(to get y in principal range of sin^-1 x)

i.e.,

y = π - x

From the last problem we see that and

So, y is not differentiable at

Extending this, we can say that y is not differentiable at x = (2n+1)

So, for

(Ans)