A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{\tan }^{-1}}2\]
Correct Answer: D
Solution :
\[2\,{{\tan }^{-1}}\frac{1}{3}+{{\tan }^{-1}}\frac{1}{2}={{\tan }^{-1}}\left( \frac{\frac{2}{3}}{1-\frac{1}{9}} \right)+{{\tan }^{-1}}\left( \frac{1}{2} \right)\] \[={{\tan }^{-1}}\left( \frac{\frac{2}{3}}{\frac{8}{9}} \right)+{{\tan }^{-1}}\left( \frac{1}{2} \right)={{\tan }^{-1}}\,\left( \frac{3}{4} \right)+{{\tan }^{-1}}\left( \frac{1}{2} \right)\] \[={{\tan }^{-1}}\left( \frac{\frac{1}{2}+\frac{3}{4}}{1-\frac{1}{2}\times \frac{3}{4}} \right)={{\tan }^{-1}}(2)\].
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