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JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank Critical Thinking

  • question_answer
    If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi \], then \[x+y+z\] is equal to  [Kerala (Engg.) 2002]

    A) xyz

    B) 0

    C) 1

    D) 2xyz

    Correct Answer: A

    Solution :

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


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