A) \[\pi \]
B) \[\frac{\pi }{2}\]
C) 0
D) None of these
Correct Answer: B
Solution :
\[{{\tan }^{-1}}\left( \frac{xy}{zr} \right)+{{\tan }^{-1}}\left( \frac{yz}{xr} \right)+{{\tan }^{-1}}\left( \frac{xz}{yr} \right)\] \[={{\tan }^{-1}}\left[ \frac{\frac{xy}{zr}+\frac{yz}{xr}+\frac{xz}{yr}-\frac{xyz}{{{r}^{3}}}}{1-\left( \frac{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}{{{r}^{2}}} \right)} \right]={{\tan }^{-1}}\infty =\frac{\pi }{2}\].
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