ExamBro
ExamBro
MHT CET · Maths · Inverse Trigonometric Functions

If \(\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}\), then the value of \(\cos ^{-1} x+\sin ^{-1} y\) is

  1. A \(\frac{\pi}{10}\)
  2. B \(\frac{7\pi}{10}\)
  3. C \(\frac{9\pi}{10}\)
  4. D \(\frac{3\pi}{10}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{7\pi}{10}\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{ll} & \sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10} \\ \therefore \quad & \frac{\pi}{2}-\cos ^{-1} x+\frac{\pi}{2}-\sin ^{-1} y=\frac{3 \pi}{10} \\ \therefore \quad & \pi-\cos ^{-1} x-\sin ^{-1} y=\frac{3 \pi}{10} \\ \therefore \quad & \cos ^{-1} x+\sin ^{-1} y=\pi-\frac{3 \pi}{10}=\frac{7 \pi}{10}\end{array}\)