A) ?1
B) 1
C) \[-{{a}^{2}}\]
D) \[{{a}^{2}}\]
Correct Answer: A
Solution :
\[y=a{{\sin }^{4}}\theta \] Þ \[\frac{dy}{d\theta }=4a{{\sin }^{3}}\theta \cos \theta \] and \[x=a{{\cos }^{4}}\theta \] Þ \[\frac{dx}{d\theta }=-4a{{\cos }^{3}}\theta \sin \theta \] \ \[\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{-{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }=-{{\tan }^{2}}\theta \] \ \[{{\left( \frac{dy}{dx} \right)}_{\theta =\frac{3\pi }{4}}}=-{{\tan }^{2}}\left( \frac{3\pi }{4} \right)=-1\].
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