A) \[\frac{17}{6}\]
B) \[\frac{22}{15}\]
C) \[\frac{16}{5}\]
D) \[\frac{16}{9}\]
Correct Answer: A
Solution :
\[\tan \left( {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right)\] \[=\tan \left( {{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{2}{3} \right)\] \[=\tan \left\{ {{\tan }^{-1}}\left( \frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}\times \frac{2}{3}} \right) \right\}\] \[=\tan \left\{ {{\tan }^{-1}}\left( \frac{9+8}{12-6} \right) \right\}\] \[=\tan \left\{ {{\tan }^{-1}}\left( \frac{17}{6} \right) \right\}\] \[=\frac{17}{6}\]
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