Question

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

• A. $\begin{array}{c}\pi \end{array}$
• B. $\frac{\pi }{3}$
• C. $\begin{array}{c}\frac{2\pi }{3}\end{array}$
• D. $\begin{array}{c}\frac{\pi }{6}\end{array}$

Answer 1

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

${\sin }^{-1}x+{\sin }^{-1}y=\frac{2\pi }{3}\Rightarrow \frac{\pi }{2}-{\cos }^{-1}x+\frac{\pi }{2}-{\cos }^{-1}y=\frac{2\pi }{3}\begin{array}{c}\Rightarrow {\cos }^{-1}x+{\cos }^{-1}y=\pi -\frac{2\pi }{3}=\frac{\pi }{3}\end{array}$