Question

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

• A. $\pi$
• B. $-\pi$
• C. $\frac{\pi }{2}$
• D. None of these

Answer 1

Answer: (B)

$-\pi$

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