Differentiation Question 420
Question: If $ x=a( \cos t+\log \tan \frac{t}{2} ),y=a\sin t, $ then $ \frac{dy}{dx}= $
[RPET 1997; MP PET 2001]
Options:
A) $ \tan t $
B) $ -\tan t $
C) $ \cot t $
D) $ -\cot t $
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Answer:
Correct Answer: A
Solution:
Given that $ x=a( \cos t+\log \tan \frac{t}{2} ) $ and $ y=a\sin t $ . Differentiating with respect to t, we get $ \frac{dy}{dt}=a\cos t $
…..(i) and $ \frac{dx}{dt}=a[ -\sin t+\cot ( \frac{t}{2} )( \frac{1}{2} ){{\sec }^{2}}( \frac{t}{2} ) ] $
$ =a( -\sin t+\frac{1}{\sin t} )=a\frac{{{\cos }^{2}}t}{\sin t}=a\cos t\cot t $ …..(ii) From (ii) and (i), we get $ \frac{dy}{dx}=\tan t $ .
BETA
