Question

$co{s}^{-1}\left(\frac{15}{7}\right)+2ta{n}^{-1}\left(\frac{1}{5}\right)=$

• A. $\frac{\pi }{2}$
  
• B. $co{s}^{-1}\left(\frac{171}{221}\right)$
  
• C. $\frac{\pi }{4}$
• D. None of these

Answer 1

The correct option is D None of these

$co{s}^{-1}\left(\frac{15}{7}\right)+ta{n}^{-1}\frac{8}{15}$
$2ta{n}^{-1}\frac{1}{5}=ta{n}^{-1}\frac{5}{12}$
$\therefore$ $co{s}^{-1}\left(\frac{15}{17}\right)+2ta{n}^{-1}\left(\frac{1}{5}\right)$
$=ta{n}^{-1}\left(\frac{8}{15}\right)+ta{n}^{-1}\left(\frac{5}{12}\right)$
$ta{n}^{-1}\left(\frac{\frac{8}{15}+\frac{5}{12}}{1-\frac{40}{180}}\right)=ta{n}^{-1}\left(\frac{171}{140}\right)=co{s}^{-1}\left(\frac{140}{221}\right)$