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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

  • question_answer
    If\[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi ,\]then\[x+y+z\]is:

    A)  \[xyz\]                                

    B)         0

    C)         1                                            

    D)         \[2xyz\]

    E)        \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\]

    Correct Answer: A

    Solution :

    \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi \] \[\Rightarrow \] \[{{\tan }^{-1}}\left\{ \frac{x+y+z-xyz}{1-xy-yz-zx} \right\}=\pi \] \[\Rightarrow \]               \[x+y+z-xyz=0\] \[\Rightarrow \]                               \[x+y+z=xyz\]


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