A) ? 1
B) 1
C) 0
D) Indeterminate
Correct Answer: B
Solution :
\[y={{\cos }^{-1}}\cos (x-1),\,\,\,\,\,x>0\] \[\Rightarrow \,\,y=x-1,\] \[x>0\] and \[0\le x-1\le \pi \] \[\therefore \] \[y=x-1\], \[1\le x\le \pi +1\] we have, \[1<\frac{5\pi }{4}<\pi +1\] \[\therefore \,\,\,\,y=x-1,\] \[1\le x\le \pi +1\] and \[\,\,\frac{5\pi }{4}\in \,[\,1,\,\,\pi +1\,]\] \[{{\left. \frac{dy}{dx} \right|}_{x=\frac{5\pi }{4}}}={{\left. \begin{align} & 1 \\ & \\ \end{align} \right|}_{x=\frac{5\pi }{4}}}=1\].You need to login to perform this action.
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