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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        The period of the function\[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\]is:

    A)  \[\pi \]                                

    B)  \[\frac{\pi }{2}\]

    C)  \[2\pi \]                                              

    D)  none of these

    Correct Answer: B

    Solution :

                                    \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] \[={{({{\sin }^{2}}x+{{\cos }^{2}}x)}^{2}}-2{{\sin }^{2}}x{{\cos }^{2}}x\] \[=1-\frac{1}{2}{{(\sin 2x)}^{2}}=1-\frac{1}{2}\left[ \frac{1-\cos 4x}{2} \right]\] \[=\frac{3}{4}+\frac{1}{4}\cos 4x\] Since,\[\cos x\]is periodic with period\[2\pi \] \[\therefore \]The period off\[f(x)=\frac{2\pi }{4}=\frac{\pi }{2}\]


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