The function y= sin -1( cos x) is not differentiable at

Question

The function y= sin -1( cos x) is not differentiable at (A) π only (B) 2 π only (C) -2 π only (D) All option are correct

Tardigrade Admin · Accepted Answer

Domain for sin -1 x is, x ∈(-1,1) both values -1 and 1 are excluded Now, cos π=-1 and cos 2 π=1 Also, cos -2 π=1 Hence, sin -1( cos x) is non differentiable at π, 2 π and -2 π.

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

$π$ only

$2 π$ only

$- 2 π$ only

All option are correct

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

Q. The function y=sin−1(cosx) is not differentiable at________

π only

2π only

−2π only