Q63 / 170 · Manipal (MET) 2018 · Mathematics

$\begin{aligned} & \text { If } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi \text {, then } \\ & x+y+z \text { is }\end{aligned}$

  • Correct answer
    A
    xyz
  • B
    0
  • C
    1
  • D
    2 xyz

Solution

$\begin{aligned} & \text { } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi \\ & \Rightarrow \quad \tan ^{-1}\left\{\frac{x+y+z-x y z}{1-x y-y z-z x}\right\}=\pi \\ & \Rightarrow x+y+z-x y z=0 \Rightarrow x+y+z=x y z\end{aligned}$

Hence, the correct answer is option: 'A'.

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