Question

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

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

Answer 1

Answer: (D)

Let $cos^{-1}\,x+cos^{-1}\,y=\frac{2\pi}{7}$
$\Rightarrow \left(\frac{\pi}{2}-sin^{-1}\,x\right)+\left(\frac{\pi}{2}-sin^{-1}\,y\right)=\frac{2\pi}{7}$
$\Rightarrow sin^{-1}\,x+sin^{-1}\,y=\pi-\frac{2\pi}{7}=\frac{5\pi}{7}$