Differentiation Question 414
Question: If $ x=a(t+\sin t) $ and $ y=a(1-\cos t) $ , then $ \frac{dy}{dx} $ equals
[RPET 1996; MP PET 2002]
Options:
A) $ \tan (t/2) $
B) $ \cot (t/2) $
C) $ \tan 2t $
D) $ \tan t $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{\frac{d}{dt}[a(1-\cos t)]}{\frac{d}{dt}[a(t+\sin t)]} $
$ \frac{dy}{dx}=\frac{a\sin t}{a+a\cos t}=\frac{\sin t}{1+\cos t}=\frac{2\sin \frac{t}{2}\cos \frac{t}{2}}{2{{\cos }^{2}}\frac{t}{2}} $
$ \therefore \frac{dy}{dx}=\tan \frac{t}{2} $ .
BETA
