Inverse Trigonometric Functions Question 122
Question: If $ {{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{2\pi }{3}, $ then $ {{\cos }^{-1}}x+{{\cos }^{-1}}y= $
[EAMCET 1994]
Options:
A) $ \frac{2\pi }{3} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{6} $
D) $ \pi $
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{2\pi }{3} $
$ \Rightarrow \frac{\pi }{2}-{{\cos }^{-1}}x+\frac{\pi }{2}-{{\cos }^{-1}}y=\frac{2\pi }{3} $
Therefore $ {{\cos }^{-1}}x+{{\cos }^{-1}}y=\pi -\frac{2\pi }{3}=\frac{\pi }{3} $ .
BETA
