Inverse Trigonometric Functions Question 43
Question: If $ {{\cos }^{-1}}x+{{\cos }^{-1}}y=2\pi , $ then $ {{\sin }^{-1}}x+{{\sin }^{-1}}y $ is equal to
Options:
A) $ \pi $
B) $ -\pi $
C) $ \frac{\pi }{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\cos }^{-1}}x+{{\cos }^{-1}}y=2\pi $
$ \Rightarrow \frac{\pi }{2}-{{\sin }^{-1}}x+\frac{\pi }{2}-{{\sin }^{-1}}y=2\pi $
$ \Rightarrow \pi -({{\sin }^{-1}}x+{{\sin }^{-1}}y)=2\pi $
$ \Rightarrow {{\sin }^{-1}}x+{{\sin }^{-1}}y=-\pi $
BETA
