A) \[\frac{3\pi }{4}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{6}\]
Correct Answer: B
Solution :
[b] \[x={{e}^{\theta }}.\sin \theta \] \[\Rightarrow \,\,\,\frac{dx}{d\theta }={{e}^{\theta }}(\sin \theta +\cos \theta )\] \[y=3\,\sin \theta .\cos \theta \] \[\Rightarrow \,\,\,\,\frac{dy}{d\theta }=3\cos 2\theta \] \[\therefore \,\,\,\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{3\cos 2\theta }{{{e}^{\theta }}(\sin \theta +\cos \theta )}\] \[\Rightarrow \,\,\,\,\frac{dy}{dx}=0,\] when \[\theta =\frac{\pi }{4}\]
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