A) \[xyz\]
B) \[0\]
C) \[1\]
D) \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\]
Correct Answer: A
Solution :
Given that \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi \] \[\Rightarrow \] \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\pi -{{\tan }^{-1}}z\] \[\Rightarrow \] \[{{\tan }^{-1}}\left( \frac{x+y}{1-xy} \right)={{\tan }^{-1}}(-z)\] \[\Rightarrow \] \[\frac{x+y}{1-xy}=-z\] \[\Rightarrow \] \[x+y+z=xyz\]
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