Differentiation Question 213
Question: Differential coefficient of $ {{\tan }^{-1}}\sqrt{\frac{1-x^{2}}{1+x^{2}}} $ w.r.t. $ {{\cos }^{-1}}(x^{2}) $ is
[RPET 1996]
Options:
A) $ \frac{1}{2} $
B) $ -\frac{1}{2} $
C) 1
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y={{\tan }^{-1}}\sqrt{\frac{1-x^{2}}{1+x^{2}}} $ and $ z={{\cos }^{-1}}(x^{2}) $
Put $ x^{2}=\cos 2\theta $ ; $ \therefore y={{\tan }^{-1}}\sqrt{\frac{2{{\sin }^{2}}\theta }{2{{\cos }^{2}}\theta }}=\theta $ and $ z=2\theta $
$ \therefore \frac{dy}{dz}=\frac{dy/d\theta }{dz/d\theta }=\frac{1}{2} $ .
BETA
