Question

If ${\sin }^{-1}x+{\sin }^{-1}y=\frac{2\pi }{3}$, then ${\cos }^{-1}x+{\cos }^{-1}y=?$

• A. $\frac{2\pi }{3}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\pi$

Answer 1

The correct option is B $\frac{\pi }{3}$

Given, ${\sin }^{-1}\left(x\right)+{\sin }^{-1}\left(y\right)=\frac{2\pi }{3}$
$\frac{\pi }{2}-{\cos }^{-1}\left(x\right)+\frac{\pi }{2}-{\cos }^{-1}\left(y\right)=\frac{2\pi }{3}$
$\pi -\frac{2\pi }{3}={\cos }^{-1}\left(x\right)+{\cos }^{-1}\left(y\right)$
$\therefore {\cos }^{-1}\left(x\right)+{\cos }^{-1}\left(y\right)=\frac{\pi }{3}$