A) \[{{\tan }^{-1}}\left( 1/2 \right)\]
B) \[{{\tan }^{-1}}\left( \frac{1}{12} \right)\]
C) \[{{\tan }^{-1}}\left( \frac{2}{5} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{11}{21} \right)\]
Correct Answer: B
Solution :
\[\tan \left( \alpha -\beta \right)=\frac{\tan \alpha -\tan \beta }{1+\tan \alpha \tan \beta }=\frac{\frac{1}{2}-\frac{2}{5}}{1+\frac{1}{2}\times \frac{2}{5}}\] \[=\frac{1}{12}\]. \[\left\{ \because \,\tan \beta =\frac{BC}{AB}=\frac{10}{25} \right\}\]
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