A) 6/17
B) 17/6
C) 7/16
D) 16/7
Correct Answer: B
Solution :
\[\tan \,\left[ {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right]\] \[=\tan \,\left[ {{\tan }^{-1}}\frac{\sqrt{\left( 1-\frac{16}{25} \right)}}{\frac{4}{5}}+{{\tan }^{-1}}\frac{2}{3} \right]\] \[=\tan \,\left[ {{\tan }^{-1}}\left( \frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}} \right) \right]=\tan \,.\,{{\tan }^{-1}}\frac{17}{6}=\frac{17}{6}\].
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