A) \[\frac{6}{17}\]
B) \[\frac{6}{\sqrt{13}}\]
C) \[\frac{\sqrt{13}}{5}\]
D) \[\frac{17}{6}\]
Correct Answer: D
Solution :
\[\tan \left[ {{\sin }^{-1}}\left( \frac{3}{5} \right)+{{\cos }^{-1}}\left( \frac{3}{\sqrt{13}} \right) \right]\] = \[\tan \left( {{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{2}{3} \right)\] = \[\tan \left( {{\tan }^{-1}}\,\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}} \right)\] = \[\tan \left[ {{\tan }^{-1}}\frac{17}{12}\times \frac{12}{6} \right]\] = \[\frac{17}{6}\].
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