Question

If ${\sin }^{-1}x+{\cos }^{-1}y=\frac{2\pi }{5}$ , then ${\cos }^{-1}x+{\sin }^{-1}y$ is

• A. $\frac{2\pi }{5}$
• B. $\frac{3\pi }{5}$
• C. $\frac{4\pi }{5}$
• D. $\frac{3\pi }{10}$

Answer 1

Answer: (B)

Given ${\sin }^{-1}x+{\cos }^{-1}y=\frac{2\pi }{5}$
$\Rightarrow \left(\frac{\pi }{2}-{\cos }^{-1}x\right)+\left(\frac{\pi }{2}-{\sin }^{-1}y\right)=\frac{2\pi }{5}$
$\Rightarrow {\cos }^{-1}x+{\sin }^{-1}y=\pi -\frac{2\pi }{5}=\frac{3\pi }{5}$