Question

$cosec\left[2{\cot }^{-1}(5)+{\cos }^{-1}\left(\frac{4}{5}\right)\right]$ is equal to:

• A. $\frac{56}{33}$
• B. $\frac{65}{56}$
• C. $\frac{65}{33}$
• D. $\frac{75}{56}$

Answer 1

Answer: (B)

$cosec\left[2{\tan }^{-1}\left(\frac{1}{5}\right)+{\tan }^{-1}\left(\frac{3}{4}\right)\right]$
$cosec\left[{\tan }^{-1}\left(\frac{5}{12}\right)+{\tan }^{-1}\left(\frac{3}{4}\right)\right]$
$=cosec\left[{\tan }^{-1}\left(\frac{56}{33}\right)\right]=\frac{65}{56}$