A) \[{{\tan }^{-1}}\left( \frac{7}{10} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{27}{11} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{7}{5} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{1}{5} \right)\]
Correct Answer: B
Solution :
\[{{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)\] \[\Rightarrow \] \[{{\tan }^{-1}}\left( \frac{3}{4} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)\] \[={{\tan }^{-1}}\left\{ \frac{\frac{3}{4}+\frac{3}{5}}{2-\frac{3}{4}.\frac{3}{5}} \right\}={{\tan }^{-1}}\left\{ \frac{\frac{15\times 12}{20}}{\frac{20-9}{20}} \right\}\] \[={{\tan }^{-1}}\left( \frac{27}{11} \right)\]You need to login to perform this action.
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