A) \[\cos \theta \]
B) \[\tan \theta \]
C) \[\sec \theta \]
D) \[\cos ec\,\theta \]
Correct Answer: B
Solution :
\[x=a(cos\theta +\theta sin\theta )\]and \[y=a(sin\theta -\theta cos\theta )\] On differentiating w.r.t\[\theta ,\]respectively \[\frac{dx}{d\theta }=a(-sin\theta +sin\theta +\theta \,cos\theta )\] \[=a\theta \cos \theta \] and \[\frac{dy}{d\theta }=a(cos\theta +\theta sin\theta -cos\theta )\] \[=a\,\theta \sin \theta \] \[\therefore \] \[\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{a\theta \sin \theta }{a\theta \cos \theta }\] \[=\tan \theta \]
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