Differentiation Question 425
Question: If $ x=\sin t\cos 2t $ and $ y=\cos t\sin 2t $ , then at $ t=\frac{\pi }{4}, $ the value of $ \frac{dy}{dx} $ is equal to
[Pb. CET 2000]
Options:
A) -2
B) 2
C) $ \frac{1}{2} $
D) $ -\frac{1}{2} $
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Answer:
Correct Answer: C
Solution:
Let $ x=\sin t\cos 2t $ …..(i) and $ y=\cos t\sin 2t $ …..(ii) Differentiate (i) w.r.t. t, we get $ \frac{dx}{dt}=\cos t.\cos 2t-2\sin t\sin 2t $
…..(iii) Again, differentiate (ii), we get $ \frac{dy}{dt}=2\cos t\cos 2t-\sin t\sin 2t $
…..(iv) \ Dividing equation (iv) by (iii), we get $ \frac{dy}{dx}=\frac{2\cos t\cos 2t-\sin t\sin 2t}{\cos t\cos 2t-2\sin t\sin 2t} $
At $ t=\frac{\pi }{4},\frac{dy}{dx}=\frac{1}{2} $ .
BETA
