Differentiation Question 312
Question: If $ x=a\sin 2\theta (1+\cos 2\theta ),y=b\cos 2\theta (1-\cos 2\theta ) $ , then $ \frac{dy}{dx}= $
[Kurukshetra CEE 1998]
Options:
A) $ \frac{b\tan \theta }{a} $
B) $ \frac{a\tan \theta }{b} $
C) $ \frac{a}{b\tan \theta } $
D) $ \frac{b}{a\tan \theta } $
Show Answer
Answer:
Correct Answer: A
Solution:
$ x=a( \sin 2\theta +\frac{1}{2}\sin 4\theta ) $ , $ y=b( \cos 2\theta -\frac{1}{2}(1+\cos 4\theta ) ) $
$ \therefore \frac{dx}{d\theta }=2a(\cos 2\theta +\cos 4\theta )=2a.2\cos 3\theta \cos \theta $
and $ \frac{dy}{d\theta }=2b(\sin 4\theta -\sin 2\theta )=2b.2\cos 3\theta \sin \theta $
$ \therefore \frac{dy}{dx}=\frac{dy}{d\theta }\div \frac{dx}{d\theta }=\frac{b}{a}\tan \theta $ .
BETA
