A) 0
B) 1
C) \[\frac{1}{xyz}\]
D) \[xyz\]
Correct Answer: B
Solution :
\[{{\tan }^{-1}}(x)+{{\tan }^{-1}}(y)+{{\tan }^{-1}}(z)=\pi \] Þ \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\pi -{{\tan }^{-1}}z\] Þ \[\frac{x+y}{1-xy}=-z\Rightarrow x+y=-z+xyz\] Þ \[x+y+z=xyz\] Dividing by xyz, we get \[\frac{1}{yz}+\frac{1}{xz}+\frac{1}{xy}=1\]. Note: Students should remember this question as a formula.
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