Question

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

• 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

Answer: (E)

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