A) \[0\]
B) \[-1\]
C) \[\frac{2}{\sqrt{3}}\]
D) \[\frac{1}{\sqrt{3}}\]
E) 1
Correct Answer: E
Solution :
Given, \[y=\sin [{{\cos }^{-1}}\{\sin ({{\cos }^{-1}}x)\}]\] \[\Rightarrow \] \[y=som\left[ {{\cos }^{-1}}\left\{ \sin \left( \frac{\pi }{2}-{{\sin }^{-1}}x \right) \right\} \right]\] \[=\sin [{{\cos }^{-1}}(\cos {{\sin }^{-1}}x)]\] \[=\sin ({{\sin }^{-1}}x)\] \[\Rightarrow \] \[y=x\] On differentiating w.r.t.\[x,\]we get \[\frac{dy}{dx}=1\]You need to login to perform this action.
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