A) \[\frac{17}{7}\]
B) \[-\frac{17}{7}\]
C) \[\frac{7}{17}\]
D) \[-\frac{7}{17}\]
Correct Answer: D
Solution :
\[\tan \left[ 2{{\tan }^{-1}}\left( \frac{1}{5} \right)-\frac{\pi }{4} \right]=\tan \left[ {{\tan }^{-1}}\frac{\frac{2}{5}}{1-\frac{1}{25}}-{{\tan }^{-1}}(1) \right]\] \[=\tan \left[ {{\tan }^{-1}}\frac{5}{12}-{{\tan }^{-1}}(1) \right]=\tan {{\tan }^{-1}}\left( \frac{\frac{5}{12}-1}{1+\frac{5}{12}} \right)=-\frac{7}{17}\].
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