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)

${\cos }^{-1}\left(\frac{4}{5}\right)+{\tan }^{-1}\left(\frac{3}{5}\right)$
$\Rightarrow$ ${\tan }^{-1}\left(\frac{3}{4}\right)+{\tan }^{-1}\left(\frac{3}{5}\right)$
$={\tan }^{-1}\left\{\frac{\frac{3}{4}+\frac{3}{5}}{2-\frac{3}{4}.\frac{3}{5}}\right\}={\tan }^{-1}\left\{\frac{\frac{15\times 12}{20}}{\frac{20-9}{20}}\right\}$
$={\tan }^{-1}\left(\frac{27}{11}\right)$