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12th Class Mathematics Applications of Derivatives Question Bank Case Based (MCQs) - Derivatives

  • question_answer
    \[{{\sin }^{2}}x+{{\cos }^{2}}y=1\]

    A) \[\frac{\sin \,2y}{\sin \,2x}\]

    B) \[-\frac{\sin \,2x}{\sin \,2y}\]

    C) \[-\frac{\sin \,2y}{\sin \,2x}\]

    D) \[\frac{\sin \,2y}{\sin \,2x}\]

    Correct Answer: D

    Solution :

    \[{{\sin }^{2}}x+{{\cos }^{2}}y=1\] \[\Rightarrow 2\sin \,x\,cos\,x+2cos\,y\left( -\operatorname{siny}\frac{dy}{dx} \right)=0\] \[\Rightarrow \frac{dy}{dx}=\frac{-\sin 2x}{-\sin 2y}=\frac{\sin 2x}{\sin 2y}\]


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