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)