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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

  • question_answer
        \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta \]is equal to

    A)  0                                            

    B)  \[-1\]

    C)  1                                            

    D)  None of these

    Correct Answer: C

    Solution :

                    Since,\[f(x)\]is an even function \[\therefore \]  \[f(-x)=f(x),\forall \,x\in R\] On differentiating both sides w.r.t.\[x,\]we get                 \[-f-(x)=f(x)\,\,\forall \,x\in R\] \[\Rightarrow \]               \[f-(x)=-f(x)\,\,\forall \,x\in R\] Which shows that\[f(x)\]is an odd function.


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