Question

$tan\left[co{s}^{-1}\left(\frac{1}{\sqrt{82}}\right)-si{n}^{-1}\left(\frac{5}{\sqrt{26}}\right)\right]$ is equal to

• A. $\frac{2}{23}$
• B. $\frac{4}{31}$
• C. $\frac{29}{3}$
• D. $\frac{6}{13}$

Answer 1

Answer: (A)

$tan\left[co{s}^{-1}\left(\frac{1}{\sqrt{82}}\right)-si{n}^{-1}\left(\frac{5}{\sqrt{26}}\right)\right]$
$=tan\left(ta{n}^{-1}9-ta{n}^{-1}5\right)$
$=tan\left\{ta{n}^{-1}\left(\frac{9-5}{1+9\times 5}\right)\right\}=\frac{2}{23}$