JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation of implicit function Parametric

  • question_answer
    If\[x=a(\cos \theta +\theta \sin \theta )\], \[y=a(\sin \theta -\theta \cos \theta ),\text{ }\]then \[\frac{dy}{dx}=\] [DCE 1999]

    A)            \[\cos \theta \]

    B)            \[\tan \theta \]

    C)            \[\sec \theta \]

    D)            cosecq

    Correct Answer: B

    Solution :

               \[\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }\]=\[\frac{a[\cos \theta -\theta (-\sin \theta )-\cos \theta ]}{a[-\sin \theta +\theta \cos \theta +\sin \theta ]}\]                          = \[\frac{\theta \sin \theta }{\theta \cos \theta }=\tan \theta \].


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