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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    If\[y=\sin [{{\cos }^{-1}}\{\sin ({{\cos }^{-1}}x)\}],\]\[\frac{dy}{dx}\]at\[x=\frac{1}{2}\]is equal to

    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                 \[\frac{dy}{dx}=1\]


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