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)

${{\tan }^{-1}}\left( \frac{27}{11} \right)$

Answer 2

${{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)$
$\Rightarrow$ ${{\tan }^{-1}}\left( \frac{3}{4} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)$
={{\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\\}
$={{\tan }^{-1}}\left( \frac{27}{11} \right)$