Differentiation Question 265
Question: If $ y={{\sec }^{-1}}( \frac{x+1}{x-1} )+{{\sin }^{-1}}( \frac{x-1}{x+1} ) $ , then $ \frac{dy}{dx}= $
[MNR 1984]
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: A
Solution:
$ y={{\sec }^{-1}}( \frac{x+1}{x-1} )+{{\sin }^{-1}}( \frac{x-1}{x+1} ) $
or $ y={{\cos }^{-1}}\frac{x-1}{x+1}+{{\sin }^{-1}}( \frac{x-1}{x+1} ) $
$ \therefore y=\frac{\pi }{2}\Rightarrow \frac{dy}{dx}=0 $
$ ( \because {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} ) $ .
BETA
