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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    The minimum value of  \[sin{{\,}^{4}}x+co{{s}^{4}}x\]is

    A)  \[1\]            

    B)  \[0\]

    C)  \[1/2\]

    D)  None of these

    Correct Answer: C

    Solution :

    Let \[f(x)=si{{n}^{4}}x+cs{{o}^{4}}x\] \[={{({{\cos }^{2}}x+{{\sin }^{2}}x)}^{2}}-2{{\sin }^{2}}x\,{{\cos }^{2}}x\] \[=1-\frac{1}{2}\,{{\sin }^{2}}\,2x\] The maximum value of \[{{\sin }^{2}}\,2x\] is 1. \[\therefore \] The minimum value of \[f(x)\] is given by- \[f(x)=1-\frac{1}{2}(1)=\frac{1}{2}\]


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