Question

The value of ${\sin }^2\left({\cos }^{-1}\frac{1}{2}\right)+{\cos }^2\left({\sin }^{-1}\frac{1}{3}\right)$ is

• A. $\frac{17}{36}$
• B. $\frac{59}{36}$
• C. $\frac{36}{59}$
• D. None of these

Answer 1

The correct option is B $\frac{59}{36}$

The value of ${\sin }^2\left({\cos }^{-1}\frac{1}{2}\right)+{\cos }^2\left({\sin }^{-1}\frac{1}{3}\right)$

$=1-{\cos }^2\left({\cos }^{-1}\frac{1}{2}\right)+1-{\sin }^2\left({\sin }^{-1}\frac{1}{3}\right)$

$=1-{\left(\frac{1}{2}\right)}^2+1-{\left(\frac{1}{3}\right)}^2$

$=2-\frac{1}{4}-\frac{1}{9}=\frac{59}{36}$