Differentiation Question 46
Question: If $ x=2\cos t-\cos 2t $ , $ y=2\sin t-\sin 2t $ , then at $ t=\frac{\pi }{4},\frac{dy}{dx}= $
Options:
A) $ \sqrt{2}+1 $
B) $ \sqrt{2+1} $
C) $ \frac{\sqrt{2+1}}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dx}{dt}=-2\sin t+2\sin 2t $ and $ \frac{dy}{dt}=2\cos t-2\cos 2t $
Therefore $ \frac{dy}{dx}=\frac{\cos t-\cos 2t}{\sin 2t-\sin t} $
Put $ t=\frac{\pi }{4}, $ we have $ {{[ \frac{dy}{dx} ]} _{t=\pi /4}} $
$ =\frac{\cos \pi /4-\cos \pi /2}{\sin \pi /2-\sin \pi /4}=\sqrt{2}+1 $ .
BETA
