A) \[{{\tan }^{-1}}\left( \frac{33}{132} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
C) \[{{\tan }^{-1}}\left( \frac{132}{33} \right)\]
D) None of these
Correct Answer: D
Solution :
\[{{\tan }^{-1}}\left( \frac{1}{11} \right)+{{\tan }^{-1}}\left( \frac{2}{12} \right)\] = \[{{\tan }^{-1}}\left( \frac{\frac{1}{11}+\frac{2}{12}}{1-\frac{1}{11}\times \frac{2}{12}} \right)={{\tan }^{-1}}\left( \frac{12+22}{130} \right)\] = \[{{\tan }^{-1}}\left( \frac{34}{130} \right)={{\tan }^{-1}}\left( \frac{17}{65} \right)\].
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