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