If $sin^{-1}x+sin^{-1}y=\frac{2\pi}{3}, $ then the value of $cos^{-1}x+cos^{-1}y$ is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{\pi}{3}$
$\cos^{-1}x+\cos^{-1}y=\frac{π}{2}-\sin^{-1}x+\frac{π}{2}-\sin^{-1}y$
$=π-(\sin^{-1}x+\sin^{-1}y)$
$=π-\frac{2π}{3}=\frac{π}{3}$