A) \[{{\tan }^{-1}}a-{{\tan }^{-1}}b\]
B) \[{{\tan }^{-1}}a-{{\tan }^{-1}}c\]
C) \[{{\tan }^{-1}}b-{{\tan }^{-1}}c\]
D) \[{{\tan }^{-1}}c-{{\tan }^{-1}}a\]
Correct Answer: B
Solution :
\[{{\tan }^{-1}}\left( \frac{a-b}{1+ab} \right)+{{\tan }^{-1}}\left( \frac{b-c}{1+bc} \right)\] \[={{\tan }^{-1}}(a)-{{\tan }^{-1}}(b)+{{\tan }^{-1}}(b)-{{\tan }^{-1}}(c)\] \[={{\tan }^{-1}}(a)-{{\tan }^{-1}}(c)\].
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