Question

Find the value of $ {{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right) $ .

• 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) $

Answer 1

Answer: (B)

$ {{\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) $