Question

The value of $si{n}^2\left(co{s}^{-1}\frac{1}{2}\right)+co{s}^2\left(si{n}^{-1}\frac{1}{3}\right)$ is

• A.
  
• B.
  
• C.
  
• D. None of these

Answer 1

The correct option is B

$si{n}^2\left(co{s}^{-1}\frac{1}{2}\right)+co{s}^2\left(si{n}^{-1}\frac{1}{3}\right)$
$=1-co{s}^2\left(co{s}^{-1}\frac{1}{2}\right)+1-si{n}^2\left(si{n}^{-1}\frac{1}{3}\right)$
$=1-{\left(\frac{1}{2}\right)}^2+1-{\left(\frac{1}{3}\right)}^2=2-\frac{1}{4}-\frac{1}{9}=\frac{59}{36}$