Differentiation Question 325
Question: If $ y={{\tan }^{-1}}(\sec x-\tan x) $ then $ \frac{dy}{dx}= $
[Karnataka CET 2004]
Options:
A) 2
B) -2
C) ½
D) -1/2
Show Answer
Answer:
Correct Answer: B
Solution:
$ y={{\tan }^{-1}}(\sec x-\tan x) $
$ \frac{dy}{dx}=\frac{1}{1+{{(\sec x-\tan x)}^{2}}}(\sec x\tan x-{{\sec }^{2}}x) $
$ \frac{dy}{dx}=\frac{{{\cos }^{2}}x.{{\sec }^{2}}x(\sin x-1)}{{{(1-\sin x)}^{2}}+{{\cos }^{2}}x} $
$ \frac{dy}{dx}=\frac{\sin x-1}{1-2\sin x+{{\sin }^{2}}x+{{\cos }^{2}}x}=\frac{\sin x-1}{2(1-\sin x)}=-\frac{1}{2}. $
BETA
