A) \[6\]
B) \[17/6\]
C) \[6/17\]
D) None of these
Correct Answer: D
Solution :
\[\tan \left[ {{\cos }^{-1}}\left( \frac{3}{5} \right)+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]\] \[=\tan \left[ {{\sec }^{-1}}\left( \frac{5}{3} \right)+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]\] \[=\tan \left[ {{\tan }^{-1}}\sqrt{-1+{{\left( \frac{5}{3} \right)}^{2}}}+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]\] \[=\tan \left[ {{\tan }^{-1}}\left( \frac{4}{3} \right)+{{\tan }^{-1}}\left( \frac{2}{3} \right) \right]\] \[=\tan \left[ {{\tan }^{-1}}\left( \frac{\frac{4}{3}+\frac{2}{3}}{1-\frac{4}{3}.\frac{2}{3}} \right) \right]=\frac{\frac{6}{3}}{\frac{1}{9}}\] \[\Rightarrow \] \[\frac{6}{3}\times 9=18\]
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