Question

If ${\cos }^{-1}x+{\cos }^{-1}y=\frac{2\pi }{7}$, then the value of ${\sin }^{-1}x+{\sin }^{-1}y=$

• A. $\frac{4\pi }{7}$
• B. $\frac{3\pi }{7}$
• C. $\frac{2\pi }{7}$
• D. $\frac{6\pi }{7}$
• E. $\frac{5\pi }{7}$

Answer 1

The correct option is E $\frac{5\pi }{7}$

Given, ${\cos }^{-1}x+{\cos }^{-1}y=\frac{2\pi }{7}$
$\Rightarrow \frac{\pi }{2}-{\sin }^{-1}x+\frac{\pi }{2}-{\sin }^{-1}y=\frac{2\pi }{7}$
$\Rightarrow {\sin }^{-1}x+{\sin }^{-1}y=\frac{\pi }{2}+\frac{\pi }{2}-\frac{2\pi }{7}$
$\Rightarrow {\sin }^{-1}x+{\sin }^{-1}y=\frac{5\pi }{7}$