Question

If ${\cos }^{-1}x+{\cos }^{-1}y=\pi ,$ then, what is the value of ${\sin }^{-1}x+{\sin }^{-1}y$ ?

• A. 0
• B. $\pi /2$
• C. $\pi$
• D. $2\pi$

Answer 1

Answer: (A)

As given, ${\cos }^{-1}x+{\cos }^{-1}y=\pi$
Since, ${\sin }^{-1}x+{\cos }^{-1}x=\pi /2$
and ${\sin }^{-1}y+{\cos }^{-1}y=\pi /2$
$\Rightarrow \frac{\pi }{2}-{\sin }^{-1}x+\frac{\pi }{2}-{\sin }^{-1}y=\pi$
$\Rightarrow \pi -\left({\sin }^{-1}x+{\sin }^{-1}y\right)=\pi$
$\Rightarrow {\sin }^{-1}x+{\sin }^{-1}y=0$