Inverse Trigonometric Functions Question 183
Question: $ {{\sin }^{-1}}x+{{\sin }^{-1}}\frac{1}{x}+{{\cos }^{-1}}x+{{\cos }^{-1}}\frac{1}{x}= $
Options:
A) $ \pi $
B) $ \frac{\pi }{2} $
C) $ \frac{3\pi }{2} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{\sin }^{-1}}x+{{\sin }^{-1}}\frac{1}{x}+{{\cos }^{-1}}x+{{\cos }^{-1}}\frac{1}{x} $ = $ {{{\sin }^{-1}}(x)+{{\cos }^{-1}}(x)}+{ {{\sin }^{-1}}( \frac{1}{x} )+{{\cos }^{-1}}( \frac{1}{x} ) } $
$ =\frac{\pi }{2}+\frac{\pi }{2}=\pi $ .
BETA
