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Q. The function $y=\sin ^{-1}(\cos x)$ is not differentiable at________

AP EAMCETAP EAMCET 2020

Solution:

Domain for $\sin ^{-1} x$
is, $x \in(-1,1)$ both values $-1$ and $1$ are excluded
Now, $\cos \pi=-1$
and $\cos 2 \pi=1$
Also, $\cos -2 \pi=1$
Hence, $\sin ^{-1}(\cos x)$ is non differentiable at $\pi, 2 \pi$ and $-2 \pi$.