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