Inverse Trigonometric Functions Question 160
Question: If $ {{\sin }^{-1}}x=\frac{\pi }{5} $ for some $ x\in (-1,1) $ , then the value of $ {{\cos }^{-1}}x $ is
[IIT 1992]
Options:
A) $ \frac{3\pi }{10} $
B) $ \frac{5\pi }{10} $
C) $ \frac{7\pi }{10} $
D) $ \frac{9\pi }{10} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} $
Therefore $ {{\cos }^{-1}}x=\frac{\pi }{2}-{{\sin }^{-1}}x=\frac{\pi }{2}-\frac{\pi }{5}=\frac{3\pi }{10} $ .
BETA
