Q99 / 180 · KCET 2018 · Mathematics

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

  • A
    \( \frac{2 \pi}{5} \)
  • Correct answer
    B
    \( \frac{3 \pi}{5} \)
  • C
    \( \frac{4 \pi}{5} \)
  • D
    \( \frac{3 \pi}{10} \)

Solution

Given that, \( \sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5} \rightarrow(1) \)
We know that, \( \sin ^{-1} x+\cos ^{-1} x=\frac{I}{2} \rightarrow(2) \)
From Eqs. (1) and (2), we have
\[ \begin{array}{l} \frac{\Pi}{2}-\cos ^{-1} x+\frac{\Pi}{2}-\sin ^{-1} y=\frac{2 \Pi}{5} \\ \Rightarrow \cos ^{-1} x+\sin ^{-1} y=\Pi-\frac{2 \Pi}{5}=\frac{3 \Pi}{5} \end{array} \]

Hence, the correct answer is option: 'B'.

Relevant Questions