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} $